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Question: How to solve system of equations explicitly

Question:How to solve system of equations explicitly

ijuptilk 100 Maple
solve
July 13 2022
0

Please I need your assistance. I want to solve for c__4, c__5, c__6, and c__8  from 4 systems of the equation: See my code below:

Since there 4 equations and 4 unknowns, is it possible to get the result explicitly without setting c__6=c__8 as maple did? The solution is at the end of the maple file.

LSA.mw
 

``

> 

## "Note that I use I(t) = X(t)"" and S^(*),E^(*), I^(*), H^(*), B^(*), D^(*), R^(*), P^(*) = (`S__1`,`E__1`,`I__1`,`H__1`,`B__1`,`D__1`,`R__1`,`P__1`,) thorought the work."
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###
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###
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restart:
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f__1 := Delta -(psi + mu)*S(t);

Delta-(psi+mu)*S(t)

 (1)
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f__2 := psi*S(t) -(delta + mu)*E(t);

psi*S(t)-(delta+mu)*E(t)

 (2)
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f__3 := Delta*E(t) -(gamma+gamma__1 + mu)*X(t);

Delta*E(t)-(gamma+gamma__1+mu)*X(t)

 (3)
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f__4 := gamma__1*X(t)-(eta + xi + mu)*H(t);

gamma__1*X(t)-(eta+xi+mu)*H(t)

 (4)
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f__5 := xi*H(t) - mu*R(t);

xi*H(t)-mu*R(t)

 (5)
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f__6 := gamma*X(t)-eta*H(t) - d*D(t);

gamma*X(t)-eta*H(t)-d*D(t)

 (6)
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f__7 := b*D(t) - b*B(t);

b*D(t)-b*B(t)

 (7)
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f__8 := phi__p + sigma*X(t)+eta__1*H(t) +d__1*D(t)+ b__1*B(t) - alpha*P(t);

phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t)

 (8)
> 

S__1 := Delta/mu - a__1*E__1/mu: X__1:= delta*E__1/a__2: H__1 := delta*gamma__1*E__1/a__2*a__3: R__1 := delta*gamma__1*xi*E__1/a__2*a__3*mu: B__1 := 1/b*(gamma*delta/a__2 + delta*eta*gamma__1/a__2*a__3)*E__1: D__1 := 1/d*(gamma*delta/a__2 + delta*eta*gamma__1/a__2*a__3)*E__1: P__1 := (1/alpha)*(delta*sigma/a__2 + delta*eta*gamma__1/a__2*a__3 + (d__1/d - b__1/b)*(delta*gamma/a__2 + delta*eta*gamma__1/a__2*a__3))*E__1 + phi__p/alpha:
> 

M__1 := c__1*f__1*(1-S__1/S(t));

c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t))

 (9)
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M__2 := c__2*f__2*(1-E__1/E(t));

c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t))

 (10)
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M__3 := c__3*f__3*(1-X__1/X(t));

0

 (11)
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M__4 :=c__4*f__4*(1-H__1/H(t));

c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)))

 (12)
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M__5 := c__5*f__5*(1-R__1/R(t));

c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)))

 (13)
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M__6 := c__6*f__6*(1-D__1/D(t));

c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)))

 (14)
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M__7 := c__7*f__7*(1-B__1/B(t));

0

 (15)
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M__8 := c__8*f__8*(1-P__1/P(t));

0

 (16)
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restart:
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u__1 := (psi+mu)*S__1;

(psi+mu)*S__1

 (17)
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u__2 := psi*S__1;

psi*S__1

 (18)
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u__3 := delta*E__1;

delta*E__1

 (19)
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u__4 := gamma__1*X__1;

gamma__1*X__1

 (20)
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u__5 := xi*H__1;

xi*H__1

 (21)
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u__6 := gamma*X__1 + eta*H__1;

H__1*eta+X__1*gamma

 (22)
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u__7 := b*D__1;

b*D__1

 (23)
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u__8 := phi__p + sigma*X__1+eta__1*H__1 +d__1*D__1+ b__1*B__1;

B__1*b__1+D__1*d__1+H__1*eta__1+X__1*sigma+phi__p

 (24)
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M__1 := c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t));

c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t))

 (25)
> 

M__2 := c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t));

c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t))

 (26)
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M__3 := c__3*(Delta*E(t)-(gamma+gamma__1+mu)*X(t))*(1-delta*E__1/(a__2*X(t)));

c__3*(Delta*E(t)-(gamma+gamma__1+mu)*X(t))*(1-delta*E__1/(a__2*X(t)))

 (27)
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M__4 := c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)));

c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)))

 (28)
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M__5 := c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)));

c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)))

 (29)
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M__6 := c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)));

c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)))

 (30)
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M__7 := c__7*(b*D(t)-b*B(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(b*B(t)));

c__7*(b*D(t)-b*B(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(b*B(t)))

 (31)
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M__8 := c__8*(phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t))*(1-((delta*sigma/a__2+delta*eta*gamma__1*a__3/a__2+(d__1/d-b__1/b)*(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2))*E__1/alpha+phi__p/alpha)/P(t));

c__8*(phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t))*(1-((delta*sigma/a__2+delta*eta*gamma__1*a__3/a__2+(d__1/d-b__1/b)*(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2))*E__1/alpha+phi__p/alpha)/P(t))

 (32)
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J := M__1 + M__2 + M__3 + M__4 + M__5 + M__6 + M__7 + M__8;

c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t))+c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t))+c__3*(Delta*E(t)-(gamma+gamma__1+mu)*X(t))*(1-delta*E__1/(a__2*X(t)))+c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)))+c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)))+c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)))+c__7*(b*D(t)-b*B(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(b*B(t)))+c__8*(phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t))*(1-((delta*sigma/a__2+delta*eta*gamma__1*a__3/a__2+(d__1/d-b__1/b)*(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2))*E__1/alpha+phi__p/alpha)/P(t))

 (33)
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##
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L__1 := factor(expand(subs(Delta=u__1, M__1)));

-c__1*(psi+mu)*(S(t)-S__1)*(a__1*E__1+S(t)*mu-S__1*mu-psi*S__1)/(S(t)*mu)

 (34)
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L__2 := expand(subs((delta+mu)*E(t)=u__2, M__2));

c__2*psi*S(t)-c__2*psi*S(t)*E__1/E(t)-c__2*psi*S__1+c__2*psi*S__1*E__1/E(t)

 (35)
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L__3 := expand(subs((gamma+gamma__1+mu)*X(t)=u__3, M__3));

c__3*Delta*E(t)-c__3*Delta*E(t)*delta*E__1/(a__2*X(t))-c__3*delta*E__1+c__3*delta^2*E__1^2/(a__2*X(t))

 (36)
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L__4 := expand(subs((eta+xi+mu)*H(t)=u__4, M__4));

c__4*gamma__1*X(t)-c__4*gamma__1^2*X(t)*delta*E__1*a__3/(a__2*H(t))-c__4*gamma__1*X__1+c__4*gamma__1^2*X__1*delta*E__1*a__3/(a__2*H(t))

 (37)
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L__5 := expand(subs(mu*R(t)=u__5, M__5));

c__5*xi*H(t)-c__5*xi^2*H(t)*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))-c__5*xi*H__1+c__5*xi^2*H__1*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))

 (38)
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L__6 := expand(subs(d*D(t)=u__6, M__6));

c__6*gamma*X(t)-c__6*gamma^2*X(t)*E__1*delta/(d*D(t)*a__2)-c__6*gamma*X(t)*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)-c__6*eta*H(t)+c__6*eta*H(t)*E__1*gamma*delta/(d*D(t)*a__2)+c__6*eta^2*H(t)*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__6*eta*H__1+c__6*eta*H__1*E__1*gamma*delta/(d*D(t)*a__2)+c__6*eta^2*H__1*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__6*gamma*X__1+c__6*gamma^2*X__1*E__1*delta/(d*D(t)*a__2)+c__6*gamma*X__1*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)

 (39)
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L__7 := expand(subs(b*B(t)=u__7, M__7));

c__7*b*D(t)-c__7*D(t)*E__1*gamma*delta/(B(t)*a__2)-c__7*D(t)*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)-c__7*b*D__1+c__7*D__1*E__1*gamma*delta/(B(t)*a__2)+c__7*D__1*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)

 (40)
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L__8 := expand(subs(alpha*P(t)=u__8, M__8));

-c__8*sigma*X(t)*phi__p/(P(t)*alpha)-c__8*eta__1*H(t)*phi__p/(P(t)*alpha)-c__8*d__1*D(t)*phi__p/(P(t)*alpha)-c__8*b__1*B(t)*phi__p/(P(t)*alpha)+c__8*b__1*B__1*phi__p/(P(t)*alpha)-c__8*eta__1*H(t)*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*d__1*D(t)*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*b__1*B(t)*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*D__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*sigma*X(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*sigma*X(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*sigma*X(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*eta__1*H(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*eta__1*H(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*eta__1*H(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*d__1*D(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*d__1*D(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1*B(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*b__1*B(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*d__1*D__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*sigma*X(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*eta__1*H(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*eta__1*H(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1*D(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*b__1*B(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1*D__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*eta__1*H__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*sigma^2*X(t)*E__1*delta/(P(t)*alpha*a__2)+c__8*sigma^2*X__1*E__1*delta/(P(t)*alpha*a__2)-c__8*sigma*X__1-c__8*d__1*D__1-c__8*eta__1*H__1-c__8*b__1*B__1+c__8*sigma*X(t)+c__8*d__1*D(t)+c__8*eta__1*H(t)+c__8*b__1*B(t)-c__8*d__1^2*D(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*b__1^2*B(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*b__1^2*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1^2*D(t)*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1^2*B(t)*E__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1^2*B__1*E__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*phi__p/(P(t)*alpha)+c__8*eta__1*H__1*phi__p/(P(t)*alpha)+c__8*sigma*X__1*phi__p/(P(t)*alpha)-c__8*eta__1*H__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*sigma*X__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)

 (41)
> 

L := L__1 + L__2 + L__3 + L__4 + L__5 + L__6 + L__7 + L__8;

-c__1*(psi+mu)*(S(t)-S__1)*(a__1*E__1+S(t)*mu-S__1*mu-psi*S__1)/(S(t)*mu)-c__8*sigma*X(t)*phi__p/(P(t)*alpha)-c__8*eta__1*H(t)*phi__p/(P(t)*alpha)-c__8*d__1*D(t)*phi__p/(P(t)*alpha)-c__8*b__1*B(t)*phi__p/(P(t)*alpha)+c__8*b__1*B__1*phi__p/(P(t)*alpha)-c__3*Delta*E(t)*delta*E__1/(a__2*X(t))-c__7*D(t)*E__1*gamma*delta/(B(t)*a__2)+c__7*D__1*E__1*gamma*delta/(B(t)*a__2)+c__6*eta*H(t)*E__1*gamma*delta/(d*D(t)*a__2)+c__6*eta*H__1*E__1*gamma*delta/(d*D(t)*a__2)-c__7*D(t)*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)+c__7*D__1*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)-c__8*eta__1*H(t)*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*d__1*D(t)*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*b__1*B(t)*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*D__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__5*xi^2*H(t)*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__5*xi^2*H__1*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__6*eta^2*H(t)*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)+c__6*eta^2*H__1*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__6*gamma*X(t)*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)+c__6*gamma*X__1*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)-c__8*sigma*X(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*sigma*X(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*sigma*X(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*eta__1*H(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*eta__1*H(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*eta__1*H(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*d__1*D(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*d__1*D(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1*B(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*b__1*B(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*d__1*D__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*sigma*X(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*eta__1*H(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*eta__1*H(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1*D(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*b__1*B(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1*D__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*eta__1*H__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__4*gamma__1^2*X(t)*delta*E__1*a__3/(a__2*H(t))+c__4*gamma__1^2*X__1*delta*E__1*a__3/(a__2*H(t))-c__6*gamma^2*X(t)*E__1*delta/(d*D(t)*a__2)+c__6*gamma^2*X__1*E__1*delta/(d*D(t)*a__2)-c__8*sigma^2*X(t)*E__1*delta/(P(t)*alpha*a__2)+c__8*sigma^2*X__1*E__1*delta/(P(t)*alpha*a__2)-c__2*psi*S(t)*E__1/E(t)+c__2*psi*S__1*E__1/E(t)+c__3*delta^2*E__1^2/(a__2*X(t))+c__2*psi*S(t)-c__2*psi*S__1+c__3*Delta*E(t)-c__3*delta*E__1-c__4*gamma__1*X__1+c__4*gamma__1*X(t)+c__5*xi*H(t)-c__5*xi*H__1+c__6*gamma*X(t)-c__6*eta*H(t)-c__6*eta*H__1-c__6*gamma*X__1-c__7*b*D__1+c__7*b*D(t)-c__8*sigma*X__1-c__8*d__1*D__1-c__8*eta__1*H__1-c__8*b__1*B__1+c__8*sigma*X(t)+c__8*d__1*D(t)+c__8*eta__1*H(t)+c__8*b__1*B(t)-c__8*d__1^2*D(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*b__1^2*B(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*b__1^2*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1^2*D(t)*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1^2*B(t)*E__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1^2*B__1*E__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*phi__p/(P(t)*alpha)+c__8*eta__1*H__1*phi__p/(P(t)*alpha)+c__8*sigma*X__1*phi__p/(P(t)*alpha)-c__8*eta__1*H__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*sigma*X__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)

 (42)
> 

## Collecting the coefficients of X, H, D, B and E
> 

k__1 := coeff(L,X(t));

-c__8*sigma*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*sigma*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__6*gamma^2*E__1*delta/(d*D(t)*a__2)-c__8*sigma^2*E__1*delta/(P(t)*alpha*a__2)-c__4*gamma__1^2*delta*E__1*a__3/(a__2*H(t))-c__8*sigma*phi__p/(P(t)*alpha)-c__6*gamma*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)-c__8*sigma*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*sigma*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*sigma*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma+c__4*gamma__1+c__6*gamma

 (43)
> 

k__2 := coeff(L,H(t));

-c__5*xi^2*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__6*eta^2*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__8*eta__1*phi__p/(P(t)*alpha)-c__8*eta__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*eta__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*eta__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__6*eta+c__5*xi+c__8*eta__1+c__6*eta*E__1*gamma*delta/(d*D(t)*a__2)-c__8*eta__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*eta__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*eta__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)

 (44)
> 

k__3 := coeff(L, D(t));

-c__7*E__1*gamma*delta/(B(t)*a__2)-c__8*d__1^2*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1^2*E__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*d__1*phi__p/(P(t)*alpha)-c__8*d__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*d__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1+c__7*b-c__7*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)-c__8*d__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)

 (45)
> 

k__4 := coeff(L, B(t));

c__8*b__1^2*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*b__1^2*E__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1*phi__p/(P(t)*alpha)-c__8*b__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*b__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1-c__8*b__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*b__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)

 (46)
> 

k__5 := coeff(L, E(t));

-c__3*Delta*delta*E__1/(a__2*X(t))+c__3*Delta

 (47)
> 

##
> 

## L terms that not coeffiecient X, H, D, B and E
> 

W__12 := coeff(L, X(t), 0):
> 

W__1 := coeff(W__12, H(t), 0):
> 

W__11 := coeff(W__1, D(t), 0):
> 

W__12 := coeff(W__11, B(t), 0):
> 

k__6 := coeff(W__12, E(t), 0);

-c__1*(psi+mu)*(S(t)-S__1)*(a__1*E__1+S(t)*mu-S__1*mu-psi*S__1)/(S(t)*mu)+c__8*b__1*B__1*phi__p/(P(t)*alpha)+c__8*b__1*B__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*D__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__5*xi^2*H__1*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__8*b__1*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*d__1*D__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1*D__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*eta__1*H__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*sigma^2*X__1*E__1*delta/(P(t)*alpha*a__2)+c__2*psi*S(t)-c__2*psi*S__1-c__3*delta*E__1-c__4*gamma__1*X__1-c__5*xi*H__1-c__6*eta*H__1-c__6*gamma*X__1-c__7*b*D__1-c__8*sigma*X__1-c__8*d__1*D__1-c__8*eta__1*H__1-c__8*b__1*B__1-c__8*b__1^2*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*b__1^2*B__1*E__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*phi__p/(P(t)*alpha)+c__8*eta__1*H__1*phi__p/(P(t)*alpha)+c__8*sigma*X__1*phi__p/(P(t)*alpha)-c__8*eta__1*H__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*sigma*X__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)

 (48)
> 

## from k__5, c__3 = 0 and choose c__1 = c__2 and c__3 =c__7
> 

c__3 := 0:  c__7:=0:
> 

k__1;

-c__8*sigma*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*sigma*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__6*gamma^2*E__1*delta/(d*D(t)*a__2)-c__8*sigma^2*E__1*delta/(P(t)*alpha*a__2)-c__4*gamma__1^2*delta*E__1*a__3/(a__2*H(t))-c__8*sigma*phi__p/(P(t)*alpha)-c__6*gamma*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)-c__8*sigma*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*sigma*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*sigma*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma+c__4*gamma__1+c__6*gamma

 (49)
> 

k__2;

-c__5*xi^2*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__6*eta^2*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__8*eta__1*phi__p/(P(t)*alpha)-c__8*eta__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*eta__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*eta__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__6*eta+c__5*xi+c__8*eta__1+c__6*eta*E__1*gamma*delta/(d*D(t)*a__2)-c__8*eta__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*eta__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*eta__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)

 (50)
> 

k__3;

-c__8*d__1^2*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1^2*E__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*d__1*phi__p/(P(t)*alpha)-c__8*d__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*d__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1-c__8*d__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)

 (51)
> 

k__4;

c__8*b__1^2*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*b__1^2*E__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1*phi__p/(P(t)*alpha)-c__8*b__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*b__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1-c__8*b__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*b__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)

 (52)
> 

## Also choose

> 

sys := solve({k__1=0, k__2 =0, k__3=0, k__4=0}, [c__4,c__5, c__6, c__8]);

[[c__4 = -H(t)*gamma*(E__1*a__3*delta*eta*gamma__1+E__1*gamma*delta-D(t)*a__2*d)*c__6/(D(t)*d*gamma__1*(E__1*a__3*delta*gamma__1-H(t)*a__2)), c__5 = R(t)*eta*(E__1*a__3*delta*eta*gamma__1+E__1*gamma*delta-D(t)*a__2*d)*c__6/(D(t)*d*xi*(E__1*a__3*delta*mu*xi*gamma__1-R(t)*a__2)), c__6 = c__6, c__8 = 0]]

 (53)
> 

#
> 

#
> 

``


 

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