Question

Solve the differential equation:
$\log \left(\frac{dy}{dx}\right)=2x-3y$

Answer 1

$\log \left(\frac{dy}{dx}\right)=2x-3y$

$\Rightarrow \frac{dy}{dx}=e^{2x-3y}$

$=\frac{dy}{dx}=\frac{e^{2x}}{e^{3y}}$

$\Rightarrow e^{3y}dy=e^{2x}dx$

Integrating both sides
$\int e^{3y}dy=\int e^{2x}dx$

$\frac{e^{3y}}{3}=\frac{e^{2x}}{2}+c$