Using dsolve() to symbolically find the solution of nonlinear differential equation

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Saurabh Das
Saurabh Das 2020-5-23
I have been trying to solve a nonlinear differential equation symbolically. The below code is what I have been trying to execute. But, the final answer does not has 's' in it besides being a piecewise solution. It would be greatly appreciated if you could show me a way forward on this.
clear all
clc
syms u(s) s C n h t_c
Du = diff(u,s);
eqn = diff(u,s,3) == [(C/h)^2]*diff(u,s,1)*[(u/t_c)^(n-1)]*n;
cond1 = u(0) == 0;
cond2 = Du(0) == 0;
conds = [cond1, cond2];
sol(s) = dsolve(eqn,conds)

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