Question

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

• A. $\frac{x}{y}+e^{x^3}=C$
• B. $\frac{x}{y}-e^{x^3}=0$
• C. $-\frac{x}{y}+e^{x^3}=C$
• D. None of these

Answer 1

Answer: (A)

Given differential equation can be written as
$\frac{ydx-xdy}{y^2}+3x^2{e}^{x^3}dx=0\Rightarrow d\left(\frac{x}{y}\right)+d\left(e^{x^3}\right)=0$
$\Rightarrow \frac{x}{y}+e^{x^3}=C$