Question #236283

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

Explain the problem with step by step process?

Expert's answer

The provided equation is: PDE "px+qy+z=xq\u00b2"

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}\\\\\n\nds=\\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 \\\\\n\nz(x,y) = Cx + Dy + E"

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