Question

Find the complete solution of the given pde p^2x+q^2y=z ​

Answer 1

Step-by-step explanation:

2

x + q

2

y = u. (11)

Solution. To find a general solution, we proceed as follows:

• Step 1: (Computing fx , fy , fu, fp, fq).

Set f ≡ p

2

x + q

2

y − u = 0. Then

fx = p

2

, fy = q

2

, fu = −1, fp = 2px, fq = 2qy,

and hence,

pfp + qfq = 2p

2

x + 2q

2

y, −(fx + pfu) = −p

2 + p,

−(fy + qfu) = −q

2 + q.

IIT Guwahati MA201(2016):PDE