# Solve differential equation y'+2y=y^2

Solve differential equation${y}^{\prime }+2y={y}^{2}$
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Lacey-May Snyder

${y}^{\prime }+2y={y}^{2}$
$dy/dx={y}^{2}-2y$
$dy/dx=y\left(y-2\right)$
$dy/\left(y\left(y-2\right)\right)=dx$
Integrating both sides
$\int dy/\left(y\left(y-2\right)\right)=\int dx$
$2/2\int dy/\left(y\left(y-2\right)\right)=\int dx$
$1/2\int 2/\left(y\left(y-2\right)\right)dy=\int dx$

Separating each parts
$1/2\int \left(y/\left(y\left(y-2\right)\right)-\left(\left(y-2\right)\right)/\left(y\left(y-2\right)\right)\right)dy=\int dx$
$\int 1/\left(y-2\right)dy-\int 1/ydy=2\int dx$
$\mathrm{ln}\left(y-2\right)-\mathrm{ln}\left(y\right)=2x+C$
$\mathrm{ln}\left(\left(y-2\right)/y\right)=2x+C$
$\left(y-2\right)/y={e}^{2x+C}$
$={e}^{2x\ast {e}^{C}}$
$={e}^{2x}C$
Where C is an arbitrary constant
$\left(y-2\right)/y={e}^{2x}C$

###### Not exactly what you’re looking for?
Jeffrey Jordon

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee