Question

solve z^2=pqxy using charpit's method

Answer 1

Here is your solution. perform

pdp−qdq

pq(qy−px)

=−

ydx−xdy

xy(px−qy)

pdp−qdqpq(qy−px)=−ydx−xdyxy(px−qy)

resulting to

d(pq)

pq

=

d(xy)

xy

d(pq)pq=d(xy)xy

Integrating we get

logpq=logxy+logc⟹

pq

xy

=c

⟹p=

cxy

q

.

logpq=logxy+logc⟹pqxy=c⟹p=cxyq.

Answer 2

Answer:

z= b(x^c)(y^(1/c)) where c = √a