# finidng the general solution

• Feb 9th 2010, 02:01 PM
bobguy
finidng the general solution
Find the general solution of the equation:

1= [3y*cos(y^2)*dy/dx] + [3e^(-x) * ycos(y^2) * dy/dx]

really really stuck on this, any help would be appreciated!
• Feb 9th 2010, 04:35 PM
Jester
Quote:

Originally Posted by bobguy
Find the general solution of the equation:

1= [3y*cos(y^2)*dy/dx] + [3e^(-x) * ycos(y^2) * dy/dx]

really really stuck on this, any help would be appreciated!

If you factor the RHS you get

$
1 = 3y \cos \left(y^2\right) \left(1 + e^{-x}\right) \frac{dy}{dx}
$

at which point we recognize this is separable, so

$
\frac{dx}{1+e^{-x}} = 3y \cos \left(y^2\right)dy
$

or

$
\frac{e^x\,dx}{e^{x}+1} = 3y \cos \left(y^2\right)dy
$
.

Now integrate each side.