(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'd like to solve the following non-homogeneous second order differential equation and may

I ask smart scholars out there to help me with this?

y"(1-1.5(y')^2)=Cx^n, (^ denotes "to the power of")

where C and n are constants, and the boundary conditions are:

y=0 at x=0,

y'=0 at x=L/2 (L is between 100 and 200).

Thanks.

2. Relevant equations

3. The attempt at a solution

Indtroducing v=y', the equation becomes

v'(1.0-1.5v^2)=Cx^n

Integration of the above equation provides

(v-0.5v^3)=nCx^(N+1)-const.

Employing v=0 at x=L/2, const=nC(L/2)^(n+1), and the equation becomes

v-0.5v^3=nCx^(n+1)+nC(L/2)^(n+1)

I can't go any further.

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# Homework Help: Solution of the nonlinear 2nd order differential equation

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