How to find the general solution for:
$$\alpha\frac{d^2y}{dx^2}=\beta(y^2-1)^2$$

Question

How to find the general solution for:
$$\alpha\frac{d^2y}{dx^2}=\beta(y^2-1)^2$$

amistre64 · Answer

series comes to mind ... but thats just an idea

amistre64 · Answer

what methods do you have at your disposal?  any of them seem more doable than the others?

anonymous · Answer

I seem to be looking for a hyperbolic tangent function :)

anonymous · Answer

However the solution I have is for a case without constants alpha and beta, and without derivation, so I need to figure that part out.

amistre64 · Answer

y = tanh(x)  eh, sad to say we havent covered those well enough in the classes i took :/

anonymous · Answer

They do not seem to be covered much at all :) Well I can try to introduce some constant
$$y=tanh(x)$$
and reverse-engineer the entire thing perhaps...

anonymous · Answer

ehm
so
$$y=a*tanh(bx)$$

amistre64 · Answer

thats a good enough place to start as any other :)

anonymous · Answer

I'll let you know if it leads anywhere :) Thanks

amistre64 · Answer

thnx.  i know its outta my scope of expertise to verify a solution;  but there are plenty of people on here that are definantly smarter than me that can handle it :)  good luck