The solution of the partial differential equation  is

Concept:

Xp + Yq = Z

Where

 & X, Y and Z are function of x, y & z

Then it’s auxiliary equation will be

 & on solving above we get u = c₁ & v = c₂

Where c₁ & c₂ = constants u & v are functions of x, y, z

Then solution of the above equation will be

f(u, v) = 0 or u = ϕ (v)

Calculation:

We are given

Then its auxiliary equation will be,

 ---(1)

On solving first two parts of the above equation we

We can write equation (1) as expressed below

By integrating the above equation,

In x + In y = In z + In c₂

⇒ In c₂ = In x + In y – In z

Hence solution of given equation will be

f(c₁, c₂) = 0