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. $\frac{x}{y}-e^{x^3}=c$
• C. $\frac{y}{x}+e^{x^3}=c$
• D. $\frac{y}{x}-e^{x^3}=c$

Answer 1

Answer: (A)

Divide the equation by $y^2$, we get
$\frac{ydx-xdy}{y^2}=-3x^2{e}^{x^3}dx$
$\Rightarrow \frac{d}{dx}\left(\frac{x}{y}\right)=-\frac{d}{dx}\left(e^{x^3}\right)$
On integrating we get,
$\frac{x}{y}=-e^{x^3}+c$
$\Rightarrow \frac{x}{y}+e^{x^3}=c$