Question

(1+x^2)dy/dx-4x=3cot inverse x ,Find differential equation.

Answer 1

( 1+x²)dy/dx -4x = 3cot^-1x

(1 +x²)dy/dx = (4x +3cot^-1x)

dy = (4x+ 3cot^-1x)/(1+x²) dx


dy = 4. x/(1+x²)dx + 3cot^-1x/(1+x²)dx

now integrate

use formate
f'(x)/f(x)dx = lnf(x) + C
and
f(x) .f'(x)dx = f(x)²/2 +C

now,
y = 2ln(1+x²) -3/2(cot^-1x )² +C