solve P² + q² =Z high level PDE form 2nd
B.E student's solution please ??
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Answer:
p2y=qz−q2=a...(I)
This equation is of the form f1(x,p)=f2(y,q).
Its solution is given by dz=pdx+qdy, upon integrating this we get value of z.
From (I)
−yq2+zq−a=0, solving the quadratic equation for q, we get
q=−z±z2−4ay√−2y.
Taking the positive value only, q=−z+z2−4ay√−2y .
Also, from (I), p2y=a, therefore p=a√y.
Therfore dz=a√ydx+−z+z2−4ay√−2ydy .
I can't get any further. I know, how to solve by charpit's method, but my book mentions that I solve it without using charpit.
The answer is given: z2=(cx+a)2+c2y2
hope it's helpful
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