Question

5) Find the particular integral of ∂²z/∂x²-3 ∂²z/∂x∂y+∂²z/∂y²= 2x sin y.

Explain the problem with step by step process?

Answer 1

z=x²y+6xy³+cos(xy²)

∂z/∂x=2xy+6y³-y²sin(xy²)

∂z/∂y=x²+18xy²-2xysin(xy²)

∂²z/∂x²=2y-y⁴cos(xy²)

∂²z/∂x∂y=2x+18y²-2ysin(xy²)-2xy³cos(xy²)

∂²z/∂y²=36xy-2xsin(xy²)-4xy²cos(xy²)