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**Altair** We have started PDEs in our MAth course in BE ME. We are following Kreyszig and I had problem understanding the basic concepts. It says "PDEs SOLVABLE AS ODEs : It happens if a PDE involves derivatives with respect to one variable only (or can be transformed to such a form), so that the other variable9s) can be treasted as parameters(s)"

There's an example I am confused in,

u_xy = -u_x where $\displaystyle u=u(x,y)$

The steps goes as,

$\displaystyle u_x = p$, $\displaystyle p_y = -1$, $\displaystyle \frac{p_y}{p}=-1$, **$\displaystyle lnp=-y +c(x)$ and by integration with respect to x, **

**$\displaystyle u(x,y) = f(x)e^-y + g(y)$ where $\displaystyle f(x) = \int c(x) dx $**

I do not understand the bold part and the natural log step how does $\displaystyle y$ come in ?