- #1
younginmoon
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Homework Statement
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.
Homework Equations
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.