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Popular >

(dx)/(dt)=e^{-kt}

Solution

\frac{d x}{d t} = e^{- k t}

Solution

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

Solution steps

\frac{d x}{d t} = e^{- k t}

Substitute

\frac{d x}{d t}

with

x^{'} (t)

x^{^{'}} (t) = e^{- k t}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

x = \int e^{- k t} d t

\int e^{- k t} d t = - \frac{1}{k} e^{- k t} + c_{1}

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

Simplify

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

Popular Examples

area x^2,x^3 area

x^{2}, x^{3}

(\partial)/(\partial y)((x^2+y^2)^{3/2})

\frac{\partial}{\partial y} ((x^{2} + y^{2})^{\frac{3}{2}})

(\partial)/(\partial x)(arctan(y/(x+a)))

\frac{\partial}{\partial x} (arctan (\frac{y}{x + a}))

tangent of f(x)=8x^2-x^3,\at x=1 tangent of

f (x) = 8 x^{2} - x^{3}, at x = 1

integral of-x^2+5x-4

\int - x^{2} + 5 x - 4 d x

Frequently Asked Questions (FAQ)

What is the solution for (dx)/(dt)=e^{-kt} ?
The solution for (dx)/(dt)=e^{-kt} is x=-(e^{-kt})/k+c_{1}