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Question:"How do I solve this''?

Saha 70 Maple 18
syntax user-error
December 18 2022
0

PROBLEM-IP.mw

What to do to get an upward curve in f(eta) and downward curve in theta(eta)?I get the curve wrong.Please Help.
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restart``
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with(PDEtools):
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ODE1 := diff(f(x), x, x, x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[f(x)])*(eta*cos(omega)+f(x)*`sinω`)*(diff(f(x), x, x))+(1-phi)^2.5*M*sin(alpha)^2*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[f(x)])*Gr[x]*`cosγ`*theta = 0;

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[f(x)])*(eta*cos(omega)+f(x)*`sinω`)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin(alpha)^2*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[f(x)])*Gr[x]*`cosγ`*theta = 0

 (1)
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ODE2 := K[nf]*(diff(theta(x), x, x))/K[f]+(1/2)*Pr*(eta*cos(omega)+`sinω`*f)*(diff(theta(x), x)) = 0;

K[nf]*(diff(diff(theta(x), x), x))/K[f]+(1/2)*Pr*(eta*cos(omega)+`sinω`*f)*(diff(theta(x), x)) = 0

 (2)
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Implementation*of*Differential*Transformation*Method*(Fe[3]*O[4]-Water);

Implementation*of*Differential*DifferentialGeometry:-Transformation*Method*(Fe[3]*O[4]-Water)

 (3)
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rho[s] := 5200:
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for k from 0 to 15 do F(k+3) := -((1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[f])*(sum((m+1)*(m+2)*F(m+2)*(cos(omega)*delta(k-m+1)+sin(omega)*F(k-m)), m = 0 .. k))+(1-phi)^2.5*M*sin(alpha)^2*(1-(k+1)*F(k+1))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[f])*Gr[x]*cos*gamma*Theta(k))/((k+1)*(k+2)*(k+3)) end do:
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for k from 0 to 15 do Theta(k+2) := -(1/2)*Pr*(sum((m+1)*Theta(m+1)*(cos(omega)*delta(k-m+1)+sin(omega)*F(k-m)), m = 0 .. k))/((k+1)*(k+2)*K[nf]) end do:
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f(eta) := simplify(sum(F(i)*eta^i, i = 0 .. 5), symbolic):
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indets(f(eta));

{A, B, M, alpha, cos, eta, omega, phi, Gr[x], (1.-phi)^(1/2), sin(alpha), sin(omega)}

 (4)
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Theta(eta) := simplify(sum(Theta(i)*eta^i, i = 0 .. 5), symbolic):
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indets(Theta(eta));

{A, B, M, Pr, alpha, cos, eta, omega, phi, Gr[x], (1.-phi)^(1/2), sin(alpha), sin(omega)}

 (5)
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U := subs(M = 1, phi = .1, sin(alpha) = 1, cos(omega) = 1, sin(omega) = 0, cos*gamma = 1/sqrt(2), Gr[x] = 0, Pr = 6.2, `ρβ`[f] = 20939.1, K[nf] = .6842, f(eta));

(A-0.3201806132e-1*eta^2-0.1772797452e-1*eta^3-.1280722452*eta+0.6403612263e-1*eta^2*A)*eta^2

 (6)
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V := subs(Pr = 6.2, phi = .1, sin(alpha) = 1, M = 1, cos(omega) = 1, sin(omega) = 0, Gr[x] = 0, cos(gamma) = 1/sqrt(2), `ρβ`[f] = 20939.1, K[nf] = .6842, Theta(eta));

1.000000000+1.000000000*B*eta

 (7)
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e1 := subs(eta = 0, U) = 0;

0 = 0

  

diff*(0, 0) = 0

  

-14.09573093+12.91590125*A = 1

  

1.000000000 = 1

  

1.000000000+3.000000000*B = 0

  

{1.000000000 = 1, -14.09573093+12.91590125*A = 1, 1.000000000+3.000000000*B = 0}

  

{A = 1.168771009, B = -.3333333333}

 (8)
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U1 := subs(A = 1.168771009, B = -.3333333333, U);

(1.168771009+0.4282550234e-1*eta^2-0.1772797452e-1*eta^3-.1280722452*eta)*eta^2

 (9)
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V1 := subs(A = 1.168771009, B = -.3333333333, V);

1.000000000-.3333333333*eta

 (10)
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p1 := M = 1, phi = .1, A = 1.168771009*(1/2), B = -.3333333333, sin(alpha) = 1, cos(omega) = 1, sin(omega) = 0, cos*gamma = 1/sqrt(2), Gr[x] = 0, Pr = 6.2:
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s1 := subs(p1, f(eta)):
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d1 := diff(s1, `$`(eta, 1)):
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plot([d1, d2, d3], eta = 0 .. 1);

Warning, expecting only range variable eta in expression (.1080744102e-1*eta-.7183594026e-1*eta^2-.1280722452-.3441379740e-1*cos+.5735632896e-2*eta*cos-.3966707070e-2*eta^2*cos)*eta^2+2*(.5843855045+.540372051e-2*eta^2-.2394531342e-1*eta^3-.1280722452*eta-.3441379740e-1*eta*cos+.2867816448e-2*eta^2*cos-.1322235690e-2*eta^3*cos)*eta to be plotted but found name cos

  

 
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p1 := M = 1, phi = .1, A = 1.168771009*(1/2), B = -.3333333333, sin(alpha) = 1, cos(omega) = 1, sin(omega) = 0, cos*gamma = 1/sqrt(2), Gr[x] = 0, Pr = 6.2:
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s1 := subs(p1, Theta(eta)):
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plot([s1, s2, s3], eta = 0 .. 1);

Warning, expecting only range variable eta in expression 1.000000000-.3333333333*eta+.6611393405e-1*eta^4-.8693603699e-2*eta^5-.2336024612e-2*eta^5*cos to be plotted but found name cos

  

 
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``

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