Question

Solution of partial differential equation yzp-xzq=xy is ?

Answer 1

Answer:

Hence the general solution is (x2 + y2, x2 z2) = 0

Step-by-step explanation:

Given that yzp xzq = xy .(i)

We know that ...(2)

here P = y z, Q = - x z and R = x y

Now auxiliary equation is = =

Or, = =

Taking 1st & 2nd term, we get

=

Or, = y dy + x dx = 0

on integrating, we get

+ = c

Or, x2 + y2 = c1 ..(3)

Similarly, taking 1st & 3rd term, we get

= =

Or, x dx z dz = 0

on integrating, we get

x2 z2 = c2 .(4)

Hence the general solution is (x2 + y2, x2 z2) = 0