$$\frac{\partial u}{\partial x}(x,y)=f(x,y,u(x,y))$$
$$\frac{\partial u}{\partial y}(x,y)=g(x,y,u(x,y))$$
$$u(x_0,y_0)=u_0$$
I want to write this but as an equation, I have tried
\begin{equation}
& =\frac{\partial u}{\partial x}(x,y)=f(x,y,u(x,y))\\
& =\frac{\partial u}{\partial y}(x,y)=g(x,y,u(x,y))\\
u(x_0,y_0)=u_0
\end{equation}
but can't get it to work.
Any feedback would be greatly appreciated

$$; use\[ \]instead. 2. You can not use&inside anequation; usealigninstead ofequation. Then\frac{\partial u}{\partial x}(x,y) &= f(x,y,u(x,y))\\.alignedinsideequationthen. See: http://tex.stackexchange.com/a/171473/14757 – Sigur Jan 02 '15 at 14:19