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Popular >

(dr)/(dt)=-r

Solution

\frac{d r}{d t} = - r

Solution

r = e^{- t + c_{1}}

Solution steps

\frac{d r}{d t} = - r

Solve separable ODE:

r = e^{- t + c_{1}}

r = e^{- t + c_{1}}

Graph

Popular Examples

y = x \frac{d y}{d x}

y^'-2e^xy=-2e^x

y^{^{'}} - 2 e^{x} y = - 2 e^{x}

f(x)=3sin(5x)f^'(x)((4pi))/(15)

f (x) = 3 sin (5 x) f^{^{'}} (x) \frac{( 4 π )}{15}

y^'=(x(x^2+1))/((4y^2))

y^{^{'}} = \frac{x ( x ^{2} + 1 )}{( 4 y ^{2} )}

y^'=(x^2)/(y^2),y(1)=1

y^{^{'}} = \frac{x ^{2}}{y ^{2}}, y (1) = 1

Frequently Asked Questions (FAQ)

What is the solution for (dr)/(dt)=-r ?
The solution for (dr)/(dt)=-r is r=e^{-t+c_{1}}