What is the solution for (dx)/(dt)+3/500 x=6 ?

The solution for (dx)/(dt)+3/500 x=6 is x=-(e^{(-3t-c_{1})/(500)})/3+1000

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(dx)/(dt)+3/500 x=6

\frac{d x}{d t} + \frac{3}{500} x = 6

x = - \frac{e ^{\frac{- 3 t - c _{1}}{500}}}{3} + 1000

Solution steps

\frac{d x}{d t} + \frac{3}{500} x = 6

Solve separable ODE:

x = - \frac{e ^{\frac{- 3 t - c _{1}}{500}}}{3} + 1000

x = - \frac{e ^{\frac{- 3 t - c _{1}}{500}}}{3} + 1000

y^{^{'}} = 5 e^{- x - y}

\frac{d y}{d x} cos (y) + 2 x sin (y) = - 2 x

(t^{2} - 22 t + 85) \frac{d y}{d t} = y

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

y^{^{'}} + \frac{1}{3} y = 0

What is the solution for (dx)/(dt)+3/500 x=6 ?
The solution for (dx)/(dt)+3/500 x=6 is x=-(e^{(-3t-c_{1})/(500)})/3+1000