Mathematics - Differential Equation Question with Solution | TestHub

Given differential equation can be written as:
$y^2 dx-xy dy=x^3 dx$
$\Rightarrow \left(y dx-x dy\right)=\frac{x^3}{y} dx$
$\Rightarrow \frac{y dx-x dy}{y^2}={\left(\frac{x}{y}\right)}^3 dx$
$\Rightarrow \int \frac{d\left(\frac{x}{y}\right)}{{\left(\frac{x}{y}\right)}^3}= \int dx$
$\Rightarrow \frac{{\left(\frac{x}{y}\right)}^{-3+1 }}{-3+1}=x+c$

$\Rightarrow y^2=-2x^3-c{x}^2$

$\Rightarrow y^2+2x^3+c{x}^2=0$