Answer to Question #207429 in Differential Equations for Chinmay

Question

Find the partial differential equation by eliminating a and b from the equation z=ax+by+a²+b²

Answer 1

$$z=ax+by+a^2+b^2$$

Differentiating partially with respect to $x, y$ we get

$$\dfrac{\partial z}{\partial x}=p=a$$

$$\dfrac{\partial z}{\partial y}=q=b$$

Then the partial differential equation is

$$px+qy+p^2+q^2=z$$