Hi,

The first equation is $dy + ln x \, y \, dx = (4x +lny) \, dx$. It doesn't seem to matter how I move around the variables, I can't group the y terms with dy and the x terms with dx.

The second equation is $x \frac{dy}{dx} = y^2 + y^2 \, lnx$. For this one I rearranged the terms to get $\frac{1}{y^2}dy = \frac{1}{x}dx + \frac{lnx}{x} \, dx$. Solving the integrals gave me $ -\frac{1}{y} = lnx + \frac{1}{2}(lnx)^2$. I don't see the problem with this but the answer key gave me something different. Have I made an error?

Thanks.