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Can any one tell me why my equation not ...

salim-barzani 1640 Maple 2021
multiplication syntax 2dmath
October 18 2024
1 2

i use all code really sometime this is happen i can find each term seperatly without any factoring and collecting term i want all of them term by term i did all simplify code but i did't get result

> 

restart
> 

with(PDEtools)
> 

NULL
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
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F := l((V(xi)^(1/(2*m)))^(4*m-2)*(V(xi)^(1/(2*m))*((1/4)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^(1/(2*m))*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^(1/(2*m)))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+4*m((V(xi)^(1/(2*m)))^(4*m-2)*(V(xi)^(1/(2*m))*((1/4)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^(1/(2*m))*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^(1/(2*m)))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+b[5]*(V(xi)^(1/(2*m)))^(8*m)+b[4]*(V(xi)^(1/(2*m)))^(6*m)+b[3]*(V(xi)^(1/(2*m)))^(6*m)+b[2]*(V(xi)^(1/(2*m)))^(4*m)+(1/2)*b[6]*(V(xi)^(1/(2*m)))^2*(diff(V(xi), xi))^2*(2*m-1)*(V(xi)^(1/(2*m)))^(-2+2*m)/(m*V(xi)^2)+2*(V(xi)^(1/(2*m)))^(2*m-1)*((1/4)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^(1/(2*m))*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m*V(xi)^2))*m*b[6]+b[1]*(V(xi)^(1/(2*m)))^(2*m)-l*lambda = 0

l((V(xi)^((1/2)/m))^(4*m-2)*(V(xi)^((1/2)/m)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+4*m((V(xi)^((1/2)/m))^(4*m-2)*(V(xi)^((1/2)/m)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)+b[4]*(V(xi)^((1/2)/m))^(6*m)+b[3]*(V(xi)^((1/2)/m))^(6*m)+b[2]*(V(xi)^((1/2)/m))^(4*m)+(1/2)*b[6]*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2*(2*m-1)*(V(xi)^((1/2)/m))^(-2+2*m)/(m*V(xi)^2)+2*(V(xi)^((1/2)/m))^(2*m-1)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))*m*b[6]+b[1]*(V(xi)^((1/2)/m))^(2*m)-l*lambda = 0

 (2)
> 

simplify(l((V(xi)^((1/2)/m))^(4*m-2)*(V(xi)^((1/2)/m)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+4*m((V(xi)^((1/2)/m))^(4*m-2)*(V(xi)^((1/2)/m)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)+b[4]*(V(xi)^((1/2)/m))^(6*m)+b[3]*(V(xi)^((1/2)/m))^(6*m)+b[2]*(V(xi)^((1/2)/m))^(4*m)+(1/2)*b[6]*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2*(2*m-1)*(V(xi)^((1/2)/m))^(-2+2*m)/(m*V(xi)^2)+2*(V(xi)^((1/2)/m))^(2*m-1)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))*m*b[6]+b[1]*(V(xi)^((1/2)/m))^(2*m)-l*lambda = 0)

((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0

 (3)
> 

simplify(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0)

((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0

 (4)
> 

numer(lhs(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0))*denom(rhs(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0)) = numer(rhs(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0))*denom(lhs(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0))

(V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+(V(xi)^((1/2)/m))^(2*m)*V(xi)*b[1]+(V(xi)^((1/2)/m))^(6*m)*V(xi)*b[3]+(V(xi)^((1/2)/m))^(6*m)*V(xi)*b[4]+V(xi)*l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*V(xi)*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+(V(xi)^((1/2)/m))^(8*m)*V(xi)*b[5]-V(xi)*l*lambda+(V(xi)^((1/2)/m))^(2*m)*(diff(diff(V(xi), xi), xi))*b[6] = 0

 (5)
> 

simplify((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+(V(xi)^((1/2)/m))^(2*m)*V(xi)*b[1]+(V(xi)^((1/2)/m))^(6*m)*V(xi)*b[3]+(V(xi)^((1/2)/m))^(6*m)*V(xi)*b[4]+V(xi)*l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*V(xi)*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+(V(xi)^((1/2)/m))^(8*m)*V(xi)*b[5]-V(xi)*l*lambda+(V(xi)^((1/2)/m))^(2*m)*(diff(diff(V(xi), xi), xi))*b[6] = 0, 'symbolic')

V(xi)*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0

 (6)
> 

simplify(V(xi)*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0)

V(xi)*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0

 (7)
> 

normal(V(xi)*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0, ':-expanded')

V(xi)^3*b[2]+V(xi)^2*b[1]+V(xi)^4*b[3]+V(xi)^4*b[4]+V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+V(xi)^5*b[5]-V(xi)*l*lambda+V(xi)*(diff(diff(V(xi), xi), xi))*b[6] = 0

 (8)
> 

normal(V(xi)^3*b[2]+V(xi)^2*b[1]+V(xi)^4*b[3]+V(xi)^4*b[4]+V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+V(xi)^5*b[5]-V(xi)*l*lambda+V(xi)*(diff(diff(V(xi), xi), xi))*b[6] = 0)

V(xi)^3*b[2]+V(xi)^2*b[1]+V(xi)^4*b[3]+V(xi)^4*b[4]+V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+V(xi)^5*b[5]-V(xi)*l*lambda+V(xi)*(diff(diff(V(xi), xi), xi))*b[6] = 0

 (9)
> 

eval(4*%*m^2)

(4*V(xi)^3*b[2]+4*V(xi)^2*b[1]+4*V(xi)^4*b[3]+4*V(xi)^4*b[4]+4*V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+16*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)^5*b[5]-4*V(xi)*l*lambda+4*V(xi)*(diff(diff(V(xi), xi), xi))*b[6])*m^2 = 0

 (10)
> 

simplify((4*V(xi)^3*b[2]+4*V(xi)^2*b[1]+4*V(xi)^4*b[3]+4*V(xi)^4*b[4]+4*V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+16*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)^5*b[5]-4*V(xi)*l*lambda+4*V(xi)*(diff(diff(V(xi), xi), xi))*b[6])*m^2 = 0)

4*V(xi)*m^2*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0

 (11)
> 

simplify(4*V(xi)*m^2*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0, 'symbolic')

4*V(xi)*m^2*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0

 (12)
> 

normal(4*V(xi)*m^2*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0, ':-expanded')

4*V(xi)^5*m^2*b[5]+4*V(xi)^4*m^2*b[3]+4*V(xi)^4*m^2*b[4]+4*V(xi)^3*m^2*b[2]+4*V(xi)*m^2*(diff(diff(V(xi), xi), xi))*b[6]+4*V(xi)^2*m^2*b[1]+4*V(xi)*m^2*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+16*V(xi)*m^2*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a-4*V(xi)*m^2*l*lambda = 0

 (13)
 

NULL

Download simplify.mw

In exploring when number are come out ar...

salim-barzani 1640 Maple 2021
decimal
October 15 2024
2 2

When i want reploting with the parameter i make them shorter by hand, make a problem for me and give me the same graph how fixed this problem? there is any code write in begind and give me all number about 2 decimal?

> 

restart
> 

K := [alpha = .33101604, theta = -2.54098361, mu = 4.89071038, k = 5.0, A[1] = 2.70491803, a = 3.63387978]

[alpha = .33101604, theta = -2.54098361, mu = 4.89071038, k = 5.0, A[1] = 2.70491803, a = 3.63387978]

 (1)
> 

MapleTA:-Builtin:-decimal(2, 20.8571)

20.86

 (2)
> 

MapleTA:-Builtin:-decimal(2, K)

Error, (in MapleTA:-Builtin:-decimal) invalid input: round expects its 1st argument, a1, to be of type algebraic, but received [100*(alpha = .33101604), 100*(theta = -2.54098361), 100*(mu = 4.89071038), 100*(k = 5.0), 100*(A[1] = 2.70491803), 100*(a = 3.63387978)]

  
 

NULL

Download decimal.mw

How fix error in testing ode with condit...

salim-barzani 1640 Maple 2021
solve pde simplification
October 12 2024
0 2

i found thus condition which if we substitute in equation must be equal to zero, i don't know  how i can get zero

test_pde1.mw

why get Error when do seperet real and i...

salim-barzani 1640 Maple 2021
syntax 2dmath differential-equations
October 12 2024
2 2

each time i use this i did not have any problem but this equation not seperate any one know what is problem?

> 

restart
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

with(PDEtools)
> 

P := U(xi)^3*mu*C[2]*h[9]+(2*I)*(diff(U(xi), xi))*a*k*mu+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-(6*I)*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+I*U(xi)*mu^4*C[2]*h[7]-I*(diff(U(xi), xi))*v-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]-(4*(diff(U(xi), xi))*I)*k*mu^3*h[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]*I+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+2*(0+I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)) = 0

U(xi)^3*mu*C[2]*h[9]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-(6*I)*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+I*U(xi)*mu^4*C[2]*h[7]-I*(diff(U(xi), xi))*v+(2*I)*(diff(U(xi), xi))*a*k*mu-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(4*I)*(diff(U(xi), xi))*k*mu^3*h[1]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+(2*I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)) = 0

 (2)
> 

Re(P)

Re(U(xi)^3*mu*C[2]*h[9]+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(4*I)*(diff(U(xi), xi))*k*mu^3*h[1]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+(2*I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)))-Im((diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+U(xi)*mu^4*C[2]*h[7]-(diff(U(xi), xi))*v+2*(diff(U(xi), xi))*a*k*mu+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]) = 0

 (3)
 

``

Download real_and_imaginary_.mw

Transformation of strange equation In PD...

salim-barzani 1640 Maple 2021
pde differential-equations
October 11 2024
0 0

I have  a big problem in transformation How we can do suh transformation in  type of  procure  without use any hand work for example in physic abs|-| remove the exponential term how the maple remove that term automatically and collect all term and do my transformation this example is really hard one which is must do a lot by hand and mixed them which maybe a week take my time to get results and how i reach the results without spending that time i have a result of this equation and i am try to get but i don't know the results of this person is correct or not but i will share in here,  i did some try i will share in here too if in DEchange add U(xi) it will work and give me the other step but i need something more effective, when q^* is conjugate of q =exp(-ipsi(x,t))U(xi)

> 

NULL
> 

restart
> 

with(PDEtools)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)

 

 
> 

tr := {t = tau, x = xi/k+v*tau^alpha/(k*alpha)+theta, u(x, t) = U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)), u[1](x, t) = U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))}

{t = tau, x = xi/k+v*tau^alpha/(k*alpha)+theta, u(x, t) = U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)), u[1](x, t) = U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))}

 (2)
> 

pde := I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*(diff(u(x, t), `$`(x, 2)))+b*U(xi)^2*u(x, t)+C[1](h[1]*(diff(u(x, t), `$`(x, 4)))+h[2]*(diff(u(x, t), x))^2*u[1](x, t)+h[3]*abs(diff(u(x, t), x))^2*u(x, t)+h[4]*U(xi)^2*(diff(u(x, t), `$`(x, 2)))+h[5]*u(x, t)^2*(diff(u[1](x, t), `$`(x, 2)))+h[6]*U(xi)^4*u(x, t))+I*C[2]*(h[7]*(diff(u(x, t), `$`(x, 4)))+h[8]*U(xi)^2*(diff(u(x, t), x))+h[9]*u(x, t)^2*(diff(u[1](x, t), x))) = 0

I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*(diff(diff(u(x, t), x), x))+b*U(xi)^2*u(x, t)+C[1](h[1]*(diff(diff(diff(diff(u(x, t), x), x), x), x))+h[2]*(diff(u(x, t), x))^2*u[1](x, t)+h[3]*abs(diff(u(x, t), x))^2*u(x, t)+h[4]*U(xi)^2*(diff(diff(u(x, t), x), x))+h[5]*u(x, t)^2*(diff(diff(u[1](x, t), x), x))+h[6]*U(xi)^4*u(x, t))+I*C[2]*(h[7]*(diff(diff(diff(diff(u(x, t), x), x), x), x))+h[8]*U(xi)^2*(diff(u(x, t), x))+h[9]*u(x, t)^2*(diff(u[1](x, t), x))) = 0

 (3)
> 

``
> 

PDEtools:-dchange(tr, pde, [xi, tau, U, U(xi)])

I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*((2*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))-U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+b*U(xi)^3*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+C[1](h[1]*(-(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k^3-6*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))/k^2+(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(U(xi), xi), xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^4)*k^4+h[2]*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)^2*k^2*U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+h[3]*abs((exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k)^2*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+h[4]*U(xi)^2*((2*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))-U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+h[5]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))^2*((diff(diff(U(xi), xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))-(2*I)*(diff(U(xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k-U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+h[6]*U(xi)^5*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))+I*C[2]*(h[7]*(-(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k^3-6*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))/k^2+(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(U(xi), xi), xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^4)*k^4+h[8]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k+h[9]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))^2*((diff(U(xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))-I*U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k) = 0

 (4)
 

NULL


Download find_ODE.mw

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