The function is the solution of

Question

Question

This question was previously asked in

BPSC Lecturer ME Held on July 2016 (Advt. 35/2014)

Answer 1

Concept:

If a function ϕ(x_1,x₂) satisfies the Laplace equation, , then the function is the solution of the Laplace equation.

Calculation:

Given function is,

Differentiating ϕ partially with respect to x₁

Again differentiating ϕ partially with respect to x₁

Similarly, differentiating ϕ partially with respect to x₂ twice, we will get,

Adding above two equations,

As the given function satisfies the Laplace equation ∇²ϕ = 0, hence it is the solution of Laplace equation.