Question

The solution of the differential equation $ydx-xdy+3x^2{y}^2{e}^{x^3}dx=0$ is :

• A. $\frac{x}{y}+e^{x^3}=c$
• B. $\frac{x}{y}=e^{x^3}$
• C. $\frac{x}{y}+e^{x^3}=cx$
• D. $Noneofthese$

Answer 1

The correct option is A $\frac{x}{y}+e^{x^3}=c$

$ydx-xdy+3x^2{y}^2{e}^{x^3}dx=0$

$\Rightarrow ydx-xdy=-3x^2{y}^2{e}^{x^3}dx$

$\Rightarrow \frac{ydx-xdy}{y^2}=-3x^2{e}^{x^3}dx$

$\Rightarrow d\left(\frac{x}{y}\right)=-d\left(e^{x^3}\right)$

Integrating both sides
$\Rightarrow \int d\left(\frac{x}{y}\right)=-\int d\left(e^{x^3}\right)\Rightarrow \frac{x}{y}=-e^{x^3}+c\Rightarrow \frac{x}{y}+e^{x^3}=c$