What is the solution for (dv)/(dt)=10-1/100 v,v=0,t=0 ?

The solution for (dv)/(dt)=10-1/100 v,v=0,t=0 is v=-1000e^{-t/(100)}+1000

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(dv)/(dt)=10-1/100 v,v=0,t=0

\frac{d v}{d t} = 10 - \frac{1}{100} v, v = 0, t = 0

v = - 1000 e^{- \frac{t}{100}} + 1000

Solution steps

\frac{d v}{d t} = 10 - \frac{1}{100} v

Solve separable ODE:

v = - 1000 e^{- \frac{t}{100}} + 1000

v = - 1000 e^{- \frac{t}{100}} + 1000

\frac{d y}{d x} = \frac{x 4 - y ^{2}}{1 + x ^{2}}

1 + x \frac{d y}{d x} = 1 + y

2 x sin^{2} (y) d x - (x^{2} + 10) cos (y) d y = 0

\frac{d y}{d x} = cos (x) sin (y)

y^{^{'}} + 17 \frac{y}{x} = 0

What is the solution for (dv)/(dt)=10-1/100 v,v=0,t=0 ?
The solution for (dv)/(dt)=10-1/100 v,v=0,t=0 is v=-1000e^{-t/(100)}+1000