Question

Partial differential equation after eliminating arbitrary function in z=f(x^2+y^2) is​

Answer 1

Step-by-step explanation:

∂z/∂x = f'(x²+y²) . (2x)

p = 2x f' (x²+y²)

p/2x = f' (x²+y²) → 1

∂z/∂y = f' (x²+y²) . (2y)

q = 2y f' (x²+y²)

q/2y = f' (x²+y²) → 2

Divide Equation 1 & 2

1 = p/2x / q/2y

1 = 2py / 2qx

Which is the required PDE

1 = py/qx

qx = py

py - qx = 0