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

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naygarp 2018-4-14

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回答： Furqan Ahmad 2022-10-17

采纳的回答： Ngoc Thanh Hung Bui

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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?

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Ngoc Thanh Hung Bui 2018-4-15

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编辑：Ngoc Thanh Hung Bui 2018-4-15

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)

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naygarp 2018-4-16

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

Torsten 2018-4-17

I can't think of any.

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Furqan Ahmad 2022-10-17

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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.