Question

The differential equations for separable is y`- (2 + cosx)/y + 3 = 0.

\(y' - \frac{2 +cosx}{y +3}= 0\)

Answer 1

\(y' - \frac{2 +cosx}{y +3}= 0\)

\(\frac{dy}{dx} = \frac{ 2 + cosx}{y +3}\)

⇒ (y + 3)dy = 2 + (cosx)dx

Integrating on both sides

\(\frac{y^2}{2} + 3y = 2x + sinx + C\)

which is solution of given differential equation.