x^2(d^2y/dx^2) + x (dy/dx) + y = 0

Question

Verify that the given function is a solution of the differential equation.

y = 3 cos(log x) + 4 sin(log x);

x²\(\cfrac{d^2y}{dx^2} + x\cfrac{dy}{dx}+y = 0\)

x²(d²y/dx²) + x (dy/dx) + y = 0

Answer 1

y = 3 cos(log x) + 4 sin (log x) …… (1)

Differentiating both sides w.r.t. x, we get

Differentiating again w.r.t.x, we get,

Hence, y =3 cos (log x) + 4sin (log x) is a solution of the