Question

Find the particular solution of the differential equation :  dy/dx + y cot x = 2x + x² cot x, x ≠ 0. Given that y = 0, when x = pi/2

Answer 1

The given equation is a linear differential equation of the type

Hence, the solution of the differential equation is given by :

Substituting y = 0 and x = pi/2, in the above equation (i), we get

Now substituting this value in eq. (i), we get

This is the required particular solution of the given differential equation.