given the differential equation $$\left( 1-x^{2} \right) dx/dy=2y $$ , do you have to use partial fraction expansion to solve, and what is the general solution?

Question

jamesj · Answer

This equal is very clearly separable and when you do that, I don't see any terms in the denominator, do you?

jamesj · Answer

*equation

anonymous · Answer

i separated it, and i got $$dy/y=2/(1-x ^{2})dx$$ and from there im stuck

anonymous · Answer

i dont know how to integrate the right side

wasiqss · Answer

its easy , u can split into partial fraction
(1+x)(1-x)

wasiqss · Answer

then its easy

jamesj · Answer

As you've written the equation originally, you have
$$ \int (1-x^2) \ dx = \int 2y \ dy $$

jamesj · Answer

Did you invert the derivative in your original expression?

wasiqss · Answer

yehh james rite ,

anonymous · Answer

oops. yes i did

anonymous · Answer

im trying to figure out how to split 2/(1-x^2) into partial fractions but i forgot the process

wasiqss · Answer

man u made wrong equations,
james made it rite for u

anonymous · Answer

i figured it out. partial fraction expansion gives me 1/1-x + 1/1-x