Step 1: take a Calculus class and learn to integrate!
You say yourself this equation is "separable"- so separate it.
becomes
.
Now use "partial fractions" as you learned in Calculus to integrate those. That is what SlipEternal did.
Multiply both sides by
to get
. You need three equations to determine the three unknowns, A, B, and C, so substitute three different values for y to get them. If y= 0, 1= 2A. If y= 1, 1= 3A+ B+ C. If y= -1, 1= 3A+ B- C.
From 1= 2A, A= 1/2. The other two equations become 1= (3/2)+ B+ C or B+ C= 1- 3/2= -1/2 and 1= (3/2)+ B- C or B- C= 1- 3/2= -1/2. Adding those two equations 2B= -1 so B= -1/2. Subtracting 2C= 0 so C= 0 as slip eternal said.
.
On the other side you have
. (Of course, these are different "A" and "B" than before.)
Multiply on both sides by
to get
. If x= 0, that becomes
so
. If x= -3, that becomes
so
.
So your equation finally reduces to
.
Can you integrate that?