Question

An ordinary differential equation is given below:
$\left(\frac{dy}{dx}\right)\left(xlnx\right)=y$
The solution for the above equation is
(Note: $K$ denotes a constant in the options)

• A. $y=Klnx$
• B. $y=Klnx$
• C. $y=Kx{e}^x$
• D. $y=Kx{e}^{-x}$

Answer 1

The correct option is A $y=Klnx$

$\frac{dy}{dx}xlnx=y$
$\Rightarrow \int \frac{dy}{y}=\int \frac{dx}{xlnx}$
taking $lnx=t$
$\Rightarrow \frac{1}{x}dx=dt$
$\Rightarrow \int \frac{dy}{y}=\int \frac{dt}{t}$
$\Rightarrow lny=lnt+lnk$
$\Rightarrow y=kt$
$\Rightarrow y=klnx$