Question

The solution of the differential equation, $\frac{d x}{d y}=\frac{y}{2 y \ell n y+y-x}$ is

• A. $x y=y^3 \ell n y+c$
• B. $ x y=y^2 \ln y +c$
• C. $x y=y^5 \ell n y+c$
• D. $x y=y^4 \ell ny +c$

Answer 1

Answer: (B)

$ \frac{d y}{d x}=\frac{y}{2 y \ell n y+y-x} $
$\Rightarrow \frac{d x}{d y}+\frac{x}{y}=(2 \ell n y+1) $
I.F. $ e^{\int \frac{1}{y} d y}=e^{\ln y}=y$
solution is $y x=\int(2 \ell$ ny $+1) y d y+c$
$x y=y^2 \text { lny }+c$