What is the solution for (dx)/(dt)=125-x/(100),x(0)=4000 ?

The solution for (dx)/(dt)=125-x/(100),x(0)=4000 is x=-8500e^{-t/(100)}+12500

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(dx)/(dt)=125-x/(100),x(0)=4000

\frac{d x}{d t} = 125 - \frac{x}{100}, x (0) = 4000

x = - 8500 e^{- \frac{t}{100}} + 12500

Solution steps

\frac{d x}{d t} = 125 - \frac{x}{100}

Solve separable ODE:

x = - 8500 e^{- \frac{t}{100}} + 12500

x = - 8500 e^{- \frac{t}{100}} + 12500

\frac{x d x}{1 + x ^{2}} + \frac{y d y}{1 + y ^{2}} = 0

\frac{d x}{d t} = t \cdot x^{\frac{1}{2}}

\frac{d y}{d x} = \frac{cos ^{2} ( y )}{4 x - 3}

\frac{d p}{d t} = 5 p (20 - ln (p))

\frac{d y}{d x} + 2 x yy = 0, y (0) = - 1

What is the solution for (dx)/(dt)=125-x/(100),x(0)=4000 ?
The solution for (dx)/(dt)=125-x/(100),x(0)=4000 is x=-8500e^{-t/(100)}+12500