Solve the differential equation (x^2 +1) dy/dx + 2xy = 2/(x^2 - 1), where x ∈ (- ∞, -1) ⋃ (1, ∞)

Question

Solve the differential equation

\((x^2-1)\frac{dy}{dx}+2xy=\frac{2}{x^2-1},\) where x ∈ (- ∞, -1)⋃ (1, ∞ )

Answer 1

The given differential equation is \((x^2-1)\frac{dy}{dx}+2xy=\frac{2}{x^2-1}\)

⇒\(\frac{dy}{dx}+\frac{2x}{(x^2-1)}y=\frac{2}{(x^2-1)^2}\)  .....(i)

This is a linear differential equation of the form

Integrating both sides, we get

This is the required solution.