How do I get an analytical solution of a boundary value problem in MATLAB

I have the following 3rd order ordinary differential equation that I need to solve

 f'''- 1/3f'^2- 2/3ff'=0
  at x=0,  f=0; f'=1
  at x= infinity, f'=0

So how do I get the analytical solution?

Answer 1

[Ngoc Thanh Hung Bui]

I think this code is correct but it returns a empty solution for some reasons, so just use for reference

syms y(t)

Dy = diff(y);

dsolve(diff(y,3) == (1/2)*diff(y)^2 + (2/3)*diff(y)*y, y(0) == 0, Dy(0) == 1, Dy(inf) == 0)

[naygarp]

This is what Matlab returns

'Warning: Explicit solution could not be found.'

y =

[ empty sym ]

I also tried a similar approach

eqn= 'D3y-(1/3)*(Dy)^2-(2/3)*y*D2y=0';
inits= 'y(0)=0,Dy(0)=1,Dy(1)=0';
y= dsolve(eqn,inits,'x')

But no solution is obtained. Could it be that analytical solution doesn't exist?

[Torsten]

It means that MATLAB can not find an analytical expression for the solution.

[naygarp]

Is there any alternate way where I could find an analytical solution?

[Torsten]

I can't think of any.

Answer 2

[Furqan Ahmad]

Consider the linear Klein-Gordan equation utt = uxx, t > 0, −∞ < x < ∞. (5.1) subject to boundary conditions u(0, t) = u(π, t) = 0, (5.2) and initial conditions u(x, 0) = 1 + sin(x), ut(x, 0) = 0. Find the analytic solution of this given partial differential equation with initial and boundary value problem.