Q. Integrating factor of $\left( x + 2y^{3} \right)\frac{dy}{dx} = y^{2}$ is
A) $e^{\left( \frac{1}{y} \right)}$
B) $e^{- \left( \frac{1}{y} \right)}$
C) $y$
D) $\frac{- 1}{y}$
Explanation
(a)
Given differential equation can be rewritten as
$\Rightarrow$ $\frac{dx}{dy} - \frac{x}{y^{2}} = 2y$
$\therefore$ $IF = e^{- \int_{}^{}{\frac{1}{y^{2}}\ dy}} = e^{\frac{1}{y}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.