Question

Can someone please help solve this differential equation:
dy/dx=[x(y^2-1)]/[2(x-2)(x-1)]

Answer 1

Looks separable.

Answer 2

yup

Answer 3

\[\implies \frac{1}{y^2 - 1}\, dy = \frac{x}{2(x-2)(x-1)}\,dx\]

Answer 4

I've gotten it that far, it's the integrals at that point that I'm having trouble with :/

Answer 5

Yeah, they don't look particularly fun, but doable. The first one looks like a trig or hyperbolic trig function.

Answer 6

For the second, I'd look for a partial fraction decomposition.

Answer 7

thanks so much! i'll try that!

Answer 8

lhs = -tanh x

Answer 9

is the right hand side ln(x-2)-(ln(x-1)/2)?