Question

The solution of $\frac{dy}{dx} = \frac{1}{y^{2} + \sin y}$ is

• A. $x = \frac{y^{3}}{3} - \cos y + c$
• B. y + cosy = x + c
• C. $x = \frac{y^{3}}{3} + \cos y + c$
• D. None of these

Answer 1

Answer: (A)

$x = \frac{y^{3}}{3} - \cos y + c$

Answer 2

Given equation may be re-written as $dx = (y^{2} + \sin y)dy$

Integrating, $\int_{}^{}{dx} = \int_{}^{}{(y^{2} + \sin y)}dy$

∴ $x = \frac{y^{3}}{3} - \cos y + c$