ODE HELP!

[sraz]

dy/dx = (ycosx) / (1 + y^2) ; y(0) = 1

I'm confused as to where to go with this one. So far I've been able to get to this...

ln|y| + [y^2]/2 = sinx

I'm lost at this point. Sorry if I'm doing this completely wrong, any help is appreciated.

 

[galactus]

You have the worst part done.

Just let y=1 and x=0 and solve for c.

It is difficult to solve this for y, so just leave it in the form you have after you find c.

\(\displaystyle ln(y)+\frac{y^{2}}{2}=sin(x)+C\)