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(Solved):   22. Obtain the general solution of the equation \[ \left(z^{2}-2 y z-y^{2}\right) p+x(y+z) ...



22. Obtain the general solution of the equation
\[
\left(z^{2}-2 y z-y^{2}\right) p+x(y+z) q=x(y-z), \quad\left(p=z_{x}, q=z_

 

22. Obtain the general solution of the equation \[ \left(z^{2}-2 y z-y^{2}\right) p+x(y+z) q=x(y-z), \quad\left(p=z_{x}, q=z_{y}\right) \] Hence find the integral surfaces of this equation passing through (a) the \( x \)-axis, (b) the \( y \)-axis, and (c) the \( z \)-axis.


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(z2?2yz?y2)p+(xy+xz)q=xy?xz we have p=zx,q=zy (z2?2yz?y2)zx+(xy+xz)zy=xy?xz By Charpit -Lagrange method dxz2?2yz?y2=dyxy+zx=dzxy?xz
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