en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

y = - \frac{a e ^{2 a b x + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (x + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (x + c_{1})} )}

Solution steps

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

Solve separable ODE:

y = - \frac{a e ^{2 a b x + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (x + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (x + c_{1})} )}

y = - \frac{a e ^{2 a b x + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (x + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (x + c_{1})} )}

Popular Examples

integral from 1 to 2 of sqrt(4x^2-3)

\int_{1}^{2} 4 x^{2} - 3 d x

limit as x approaches 2-of kx^2

x \to 2 - lim (k x^{2})

limit as x approaches 0 of (-1)/(5x+25)

x \to 0 lim (\frac{- 1}{5 x + 25})

(\partial)/(\partial x)(2xarctan(y/z))

\frac{\partial}{\partial x} (2 x arctan (\frac{y}{z}))

limit as x approaches 1 of (inx)/(x-1)

x \to 1 lim (\frac{in x}{x - 1})

Frequently Asked Questions (FAQ)

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