Question

Solve the differential equation `x dy/dx + y = x cos x + sin x`,  given that y = 1 when `x = pi/2`

Answer 1

The given differential equation is

`x dy/dx + y = x cos x + sin x`

`=> dy/dx + y/x = (x cos x + sin x)/x`

This is a linear differential equation of the form `dy/dx + Py = Q`

Thus, the particular solution of the given differential equation is y = sinx.