Question

solve, z=px+qy-log(pq)​

Answer 1

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