# Homework Help: End of differential equation, quick alegbra Q

1. Jan 30, 2012

### csc2iffy

1. The problem statement, all variables and given/known data
I just solved a differential equation and got the problem down to its implicit solution:
y/√(1+y2) = x3+C where C is an arbitrary constant
My question now is, how can I solve for y? I can't get past the algebra. Thanks!

2. Relevant equations

3. The attempt at a solution

2. Jan 30, 2012

### Dick

Square both sides. Solve for y^2. Take a square root. Come on. Try it.

3. Jan 30, 2012

### ashwinnarayan

Square both sides and bring the bottom part to the other side. You'll get

$y^2 = (1+y^2)(x^3 + c)^2$

Then multiply out and regroup.

$y^2 -y^2(x^3 + c)^2 = (x^3 + c)^2$

then you'll get $y^2 = \frac{(x^3+c)^2}{1-(x^3+c)^2}$

So $y = \sqrt{\frac{(x^3+c)^2}{1-(x^3+c)^2}}$

4. Jan 30, 2012

thank you!