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Question: how we can find the exact solution of the problem

Question:how we can find the exact solution of the problem

Mr Haq 25 Maple 15
student
December 06 2012
0

hi,
how we get exact solution of the given system of equations correspond to boundary conditions.
and how we can plot its solution?
>restart;
with(DEtools);

ode:=[(diff(f(eta), eta$3))+beta*((diff(f(eta), eta$2))^2-f(eta)*(diff(f(eta), eta$4)))+(1+lambda)*(f(eta)*(diff(f(eta), eta$2))-(diff(f(eta), eta))^2)= 0,diff(theta(eta),eta$2)+pr*(f(eta)*diff(theta(eta),eta)+Nb*diff(theta(eta),eta$1)*diff(phi(eta),eta$1)+Nt*diff(theta(eta),eta)^2)=0,diff(phi(eta),eta$2)+Le*f(eta)*diff(phi(eta),eta$1)+Nt/Nb*diff(theta(eta),eta$2)=0];
 
Bcs := f(0) = 0, (D(f))(0) = 1, (D(f))(N) = 0, ((`@`(D, D))(f))(N) = 0, theta(0) = 1, theta(N) = 0, phi(0) = 1, phi(N) = 0;

ans := dsolve(ode, B*cs, explicit);
odetest(ans, ode); 
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