Question

The general solution of differential equation $ydx-xdy+3x^2{y}^2{e}^{x^3}dx=0$ is (where c is arbitrary constant):

• 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

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

$ydx-xdy+3x^2{y}^2{e}^{x^3}=0$
Dividing both sides by $y^2$ we get
$\frac{ydx-xdy}{y^2}+3x^2{e}^{x^3}=0$
$\therefore d\left(\frac{x}{y}\right)+d\left(e^{x^3}\right)=0$
$⟹\frac{x}{y}+e^{x^3}=c$
Hence, option 'B' is correct.