Question

The solution of the differential equation $y d x-x d y+3 x^{2} y^{2} e^{x^{3}} d x=0$ 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{y d x-x d y}{y^{2}}=-3 x^{2} e^{x^{3}} d x $
$\Rightarrow \frac{d}{d x}\left(\frac{x}{y}\right)=-\frac{d}{d x}\left(e^{x^{3}}\right)$
On integrating we get,
$\frac{x}{y}=-e^{x^{3}}+c $
$\Rightarrow \frac{x}{y}+e^{x^{3}}=c$