Answer to Question #271572 in Differential Equations for Nida

Question

Solve:

• dy/dx - 2y = 5y²

Answer 1

$\frac{dy}{dx}-2y=5y^2.$

$\frac{dy}{5y^2+2y}=dx.$

$\int{\frac{dy}{5y^2+2y}}=\int dx.$

$\int(\frac{1}{2y}-\frac{5}{2(5y+2)})dy=\int dx.$

$\frac{1}{2}\ln{\frac{y}{5y+2}}=x+C.$

$\frac{y}{5y+2}=Ce^{2x}.$

$y=\frac{2e^{2x}}{5(C-e^{2x})}=\frac{2}{5(Ce^{-2x}-1)}.$