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Popular Calculus >

(dx)/(dt)=a-bx

Solution

\frac{d x}{d t} = a - b x

Solution

x = - \frac{e ^{- b t - c_{1} b}}{b} + \frac{a}{b}

Solution steps

\frac{d x}{d t} = a - b x

Solve separable ODE:

x = - \frac{e ^{- b t - c_{1} b}}{b} + \frac{a}{b}

x = - \frac{e ^{- b t - c_{1} b}}{b} + \frac{a}{b}

Graph

Popular Examples

derivative of e^{4^x}

\frac{d}{d x} (e^{4^{x}})

sum from n=1 to infinity of 1/((n^2+5n))

n = 1 \sum \infty \frac{1}{( n ^{2} + 5 n )}

(\partial)/(\partial x)(yln(y))

\frac{\partial}{\partial x} (y ln (y))

integral of sin(8x)cos(6x)

\int sin (8 x) cos (6 x) d x

(2 ln (x))^{^{'}}

Frequently Asked Questions (FAQ)

What is the solution for (dx)/(dt)=a-bx ?
The solution for (dx)/(dt)=a-bx is x=-(e^{-bt-c_{1}b})/b+a/b