Answer to Question #223829 in Chemical Engineering for Lokika

Question #223829

The singular integral of z=xp+yq-logpq


1
Expert's answer
2021-08-16T02:19:48-0400

The complete integral of partial differential equation "z=xp+yq- logpq"

Let "F=px+qy+p^2+q^2=0" . Then by Charpit's auxiliary equations

"dpFx+pFz=dqFy+qFz=dz\u2212pFp\u2212qFq=dx\u2212Fp=dy\u2212Fq"

we have

"dp0=dq0=dz\u2212p(x+2p)\u2212q(y+2q)=dx\u2212(x+2p)=dy\u2212(y+2q) ."

This implies "p=a=constant" . Putting this in given equation, "q=\u2212y\u00b1y2\u22124(a2+ax\u2212z)"


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