Question

Solution of the differential equation $(x+2y^3)\frac{dy}{dx}=y$ is

• A. $y^3+cy=x$
• B. $x+2y^3=y+c$
• C. $y^3+cx=y$
• D. $\frac{x{y}^4}{2}+xy=cy$

Answer 1

The correct option is A $y^3+cy=x$

$(x+2y^3)\frac{dy}{dx}=y\Rightarrow \frac{dx}{dy}=\frac{x+2y^3}{y}\Rightarrow \frac{dx}{dy}-\frac{x}{y}=2y^2$

Integrating factor, I.F.
$=e^{\int (-1/y)dy}=\frac{1}{y}$
$x\times \frac{1}{y}=\int 2ydy+c\Rightarrow x=y^3+cy$