How to integrate this partial differential equation

[JulieK]

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.

 

[kevinferreira]

Yes, you should have
<br /> m(y)\frac{dy}{dx}=C(x)<br />
And therefore you can solve it by
<br /> m(y)dy=C(x)dx<br />
Which you can integrate.

 

[haruspex]

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.

You'll have to use boundary conditions. There's nothing in the equation that gives a clue about the form of C(x).