I am taking a course called partial differential equations. We are mostly learning about solving equations of the form $\phi(D_{x},D_{y})u=0$, for example $(D_{x}^{2}+D_{x}D_{y}+D_{y}^{2})u=0$ or $\frac{1}{D_{x}+D_{y}}u=0$. The thing is when I search for partial differential equations on Google I get results for mathematical equations that are different from $\phi(D_{x},D_{y})$. Does anyone know what this subject really called and if there are any good references.
thanks