Mathematics 2

Question

Find the general solutions of the following partial differential equation:
z(x-y)=px²-qy²
Solve the following equations by charpit's method:
p²+q²-2px-2qy+2xy=0
Solve the following partial differential equation:
d²z/dx²+2d²z/dxdy+d²z/dy²=x²+xy+y².

Answer 1

1. To find the general solutions of the following partial differential equation:

z(x-y)=px²-qy²

The auxiliary equations are

2. Solving by charpit's method: p²+q²-2px-2qy+2xy=0

After Integrating the required complete integral is