What is the solution for y^'=ay-by^2 ?

The solution for y^'=ay-by^2 is y=-(ae^{at+c_{1}a})/(b(1-e^{a(t+c_{1))})}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'=ay-by^2

y^{^{'}} = a y - b y^{2}

y = - \frac{a e ^{a t + c_{1} a}}{b ( 1 - e ^{a (t + c_{1})} )}

Solution steps

y^{'} (t) = a y (t) - b y (t)^{2}

Solve separable ODE:

y = - \frac{a e ^{a t + c_{1} a}}{b ( 1 - e ^{a (t + c_{1})} )}

y = - \frac{a e ^{a t + c_{1} a}}{b ( 1 - e ^{a (t + c_{1})} )}

\frac{d}{d x} (\frac{x ^{8}}{16})

\frac{d}{d t} (\frac{1}{t})

x \to 1 + lim (\frac{x + 2}{x + 1})

\int_{1}^{3} \frac{1}{x ( x + 1 )} d x

\int_{1}^{x^{2}} sin^{2} (t) d t

What is the solution for y^'=ay-by^2 ?
The solution for y^'=ay-by^2 is y=-(ae^{at+c_{1}a})/(b(1-e^{a(t+c_{1))})}