Mathematics - Differential Equation Question with Solution | TestHub

$\frac{dy}{dx}-\frac{y+3x}{\ln (y+3x)}+3=0$
$\frac{dy}{dx}+3=\frac{y+3x}{\ln (y+3x)}$
$\frac{d}{dx}(y+3x)=\frac{y+3x}{\ln (y+3x)}$
$\int \frac{\ln (y+3x)}{(y+3x)}d(y+3x)=\int dx$
Let$\ln (y+3x)=t$
$\frac{1}{(y+3x)}d(y+3x)=dt$
$\int \mathrm{tdt}=\int \mathrm{dx}$
$\frac{t^2}{2}=x+c$
$\frac{\left(\ln \right(y+3x){)}^2}{2}=x+c$