Question

The integrating factor of the differential equation $(2x+3y^2)dy=ydx(y>0)$ is

• A. $\frac{1}{x}$
• B. $\frac{1}{{}_{e}y}$
• C. $\frac{1}{y^2}$
• D. $-\frac{1}{y^2}$

Answer 1

Answer: (C)

$\left(2x+3y^2\right)dy=ydx$
$\Rightarrow \frac{2x+3y^2}{y}=\frac{dx}{dy}\Rightarrow \frac{2x}{y}+3y=\frac{dx}{dy}\Rightarrow \frac{dx}{dy}-\frac{2}{y}x=3y$
$If==e^{\int -\frac{2}{y}dy}=e^{-2logy}=e^{log{y}^{-2}}=\frac{1}{y^2}$