solve, z=px+qy-log(pq)
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Answer:
ind the complete integral of partial differential equation z=px+qy+p2+q2.
My attempt:
Let F=px+qy+p2+q2=0. Then by Charpit's auxiliary equations
dpFx+pFz=dqFy+qFz=dz−pFp−qFq=dx−Fp=dy−Fq
we have
dp0=dq0=dz−p(x+2p)−q(y+2q)=dx−(x+2p)=dy−(y+2q) .
This implies p=a=constant. Putting this in given equation, q=−y±y2−4(a2+ax−z)−−−−−−−−−−−−−−−√2
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