Question

Solve z = px+qy-2√pq
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Answer 1

Answer:

This is clairaut's form

∴ complete solution is

z=ax+by+a2−b2...(1)

Now,

∂z∂a=0⇒x+2a=0⇒a=−x2

∂z∂b=0⇒y−2b=0⇒b=y2

(1)⇒

z=−x22+y22+x24−y24

⇒y2−x24

∴ Singular solution is 4z=y2−x2