What is the solution for (dy)/(dx)=ay-by^2 ?

The solution for (dy)/(dx)=ay-by^2 is y=-(ae^{ax+c_{1}a})/(b(1-e^{a(x+c_{1))})}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=ay-by^2

\frac{d y}{d x} = a y - b y^{2}

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

Solution steps

\frac{d y}{d x} = a y (x) - b y (x)^{2}

Solve separable ODE:

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

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

8 sin (4 t) - 5 cos (4 t)

\int_{- 2}^{2} 8 1^{\frac{x}{2}} d x

\frac{( x + 3 )}{( x - 3 )}

9 y^{^{''}} - y = x e^{\frac{x}{3}}, y (0) = 1, y^{^{'}} (0) = 0

\frac{\partial}{\partial y} (\frac{y}{x} + 4 x)

What is the solution for (dy)/(dx)=ay-by^2 ?
The solution for (dy)/(dx)=ay-by^2 is y=-(ae^{ax+c_{1}a})/(b(1-e^{a(x+c_{1))})}