What is the solution for y^'=2.5-y/(2000) ?

The solution for y^'=2.5-y/(2000) is y=-e^{(-t-c_{1})/(2000)}+5000

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y^'=2.5-y/(2000)

y^{^{'}} = 2.5 - \frac{y}{2000}

y = - e^{\frac{- t - c _{1}}{2000}} + 5000

Solution steps

y^{'} (t) = 2.5 - \frac{y}{2000}

Solve separable ODE:

y = - e^{\frac{- t - c _{1}}{2000}} + 5000

y = - e^{\frac{- t - c _{1}}{2000}} + 5000

\frac{d y}{d t} + \frac{1}{2} y = 17 sin (2 t), y (0) = - 1

\int x^{- 2} + x^{\frac{1}{5}} d x

\frac{d}{d x} (arctan (s x))

\frac{d}{d x} (tan (x - y))

What is the solution for y^'=2.5-y/(2000) ?
The solution for y^'=2.5-y/(2000) is y=-e^{(-t-c_{1})/(2000)}+5000