What is the solution for (dx)/(dt)=100-x/(100),x=2000,t=0 ?

The solution for (dx)/(dt)=100-x/(100),x=2000,t=0 is x=-8000e^{-t/(100)}+10000

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(dx)/(dt)=100-x/(100),x=2000,t=0

\frac{d x}{d t} = 100 - \frac{x}{100}, x = 2000, t = 0

x = - 8000 e^{- \frac{t}{100}} + 10000

Solution steps

\frac{d x}{d t} = 100 - \frac{x}{100}

Solve separable ODE:

x = - 8000 e^{- \frac{t}{100}} + 10000

x = - 8000 e^{- \frac{t}{100}} + 10000

(\frac{y}{2}) y^{^{'}} = e^{- x}, y (0) = 4

\frac{d}{d x} (y^{2}) = 4 x^{2} + 2 x - 5

y^{2} sec (6 x) \frac{d y}{d x} = 1, y (0) = 0

y d y + x d x = 0

y^{^{'}} = 6 x y - 2 x, y (0) = 8

What is the solution for (dx)/(dt)=100-x/(100),x=2000,t=0 ?
The solution for (dx)/(dt)=100-x/(100),x=2000,t=0 is x=-8000e^{-t/(100)}+10000