The differential equation
\[
2\frac{\partial^2 z}{\partial x^2}
+
5\frac{\partial^2 z}{\partial x\partial y}
+
2\frac{\partial^2 z}{\partial y^2}
+
7\frac{\partial z}{\partial x}
+
\frac{\partial z}{\partial y}
=0
\]
is classified as
Show Hint
For PDE classification, remember only one formula:
\[
D=B^2-4AC.
\]
Positive discriminant gives Hyperbolic, zero gives Parabolic, and negative gives Elliptic.