Question

Separation of variables. Differential equation.

Answer 1

\[\begin{align*}
y\ln x\ln y\,dx+dy&=0\\\\
y\ln x\ln y\,dx&=-dy\\\\
\ln x\,dx&=-\frac{dy}{y\ln y}
\end{align*}\]
I'm guessing you're having trouble integrating?

Answer 2

Yes yes

Answer 3

I also have the same process and then im lost. haha

Answer 4

Hint: Integrate the left side by parts, the right side with a substitution. Try \(u=\ln y\).

Answer 5

so the answer would be ylny?