# How to integrate this partial differential equation

 P: 40 I have the following equation $\frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0$ where $y$ is a function of $x$ and $m$ is a function of $y$. If I integrate this equation first with respect to $y$ should I get a function of $x$ as the constant of integration (say $C\left(x\right)$) or it is just a constant? If it is a function, how can I then find its form (e.g. polynomial, etc.)? Should I use boundary conditions or I can decide about the form from inspecting the type of the equation.
 P: 123 Yes, you should have $$m(y)\frac{dy}{dx}=C(x)$$ And therefore you can solve it by $$m(y)dy=C(x)dx$$ Which you can integrate.