Math Help - first ODE course first quiz

1. first ODE course first quiz

We had a quiz and there were two versions so you didn't have the same as your neighbor
I could do the other one, but the one I was assigned seemed much more difficult
Is there something I'm missing here? because I can't seem to do this one

Find the general solution of $xsin(x+y)y' + xsin(x+y) = cos(x+y)$

2. Looks exact to me.

3. Originally Posted by jbpellerin
We had a quiz and there were two versions so you didn't have the same as your neighbor
I could do the other one, but the one I was assigned seemed much more difficult
Is there something I'm missing here? because I can't seem to do this one

Find the general solution of $xsin(x+y)y' + xsin(x+y) = cos(x+y)$
Try a change of variable, put $u=x+y$, then:

$
\frac{du}{dx}=1+\frac{dy}{dy}
$

so the equation becomes:

$x \sin(u) u'= \cos(u)$

CB