Find the particular solution of the following differential equation: dy/dx – 3y cot x = sin 2x, when y (π/2) = 2 ​

Question

Find the particular solution of the following differential equation:

\(\cfrac{dy}{dx}\)– 3y cot x = sin 2x, when y (π/2) = 2

Answer 1

\(\cfrac{dy}{dx}\) - 3y cot x = sin 2x

\(\cfrac{dy}{dx}\) = (3 cot x) y = sin 2x ……..(1)

This is the linear differential equation of the form

\(\therefore\) the solution of (1) is given by

Put sin x = t  
\(\therefore\) cos x dx = dt

This is the general solution

\(\therefore\) the particular solution is