Question

The solution of the differential equation $(x+2y^3)\frac{dy}{dx}=y,y>0$ is
(where $c$ is integration constant)

• A. $\frac{x}{y^2}=y+c$
• B. $\frac{x}{y}=y^2+c$
• C. $\frac{x^2}{y}=y^2+c$
• D. $\frac{x}{y}=x^2+c$

Answer 1

The correct option is B $\frac{x}{y}=y^2+c$

$\Rightarrow \frac{dx}{dy}-\frac{1}{y}x=2y^2$ which is linear.
On comparing with $\frac{dx}{dy}+Px=Q,$
We get, $P=\frac{-1}{y}$ and $Q=2y^2$

I.F. $=e^{\int -\frac{1}{y}dy}=e^{-\ln |y|}=\frac{1}{y}$
$\therefore$ Solution is $\frac{1}{y}x=\int \frac{1}{y}2y^{2}dy=y^2+c$
$\Rightarrow \frac{x}{y}=y^2+c$