Answer to Question #236283 in Chemical Engineering for Lokika

Question

Find the complete integral of the PDE px+qy+z=xq²

Explain the problem with step by step process?

Answer 1

The provided equation is: PDE $px+qy+z=xq²$

We can use Charpit's auxiliary equations to get: 

$ds= \frac{dp}{0}= \frac{dq}{0}=\frac{dz}{z+pq}=\frac{dx}{x+q} =\frac{dy}{y+p}\\ ds=\frac{dp}{0}, \frac{dp}{0}=\frac{dq}{0} \implies p=C, q=D$

We get a complete integral of: 

$dz = pdx + qdy = Cdx + Ddy \\ z(x,y) = Cx + Dy + E$