What is the solution for (dx)/(dt)=0.6-3/500 x ?

The solution for (dx)/(dt)=0.6-3/500 x is x=-(e^{-0.006t-c_{1}})/(0.006)+(0.6)/(0.006)

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(dx)/(dt)=0.6-3/500 x

\frac{d x}{d t} = 0.6 - \frac{3}{500} x

x = - \frac{e ^{- 0.006 t - c_{1}}}{0.006} + \frac{0.6}{0.006}

Solution steps

\frac{d x}{d t} = 0.6 - \frac{3}{500} x

Solve separable ODE:

x = - \frac{e ^{- 0.006 t - c_{1}}}{0.006} + \frac{0.6}{0.006}

x = - \frac{e ^{- 0.006 t - c_{1}}}{0.006} + \frac{0.6}{0.006}

\int (4 + x^{7})^{3} 7 x^{6} d x

5 x^{2} cos (3 x)

y^{^{''}} - \frac{7}{t} y^{^{'}} + \frac{32}{t ^{2}} y = 0

x^{2} \cdot y^{^{'}} - 4 x y = sin (3 x) \cdot x^{6}

x \to 0 lim (\frac{sin ( x ^{5} )}{x})

What is the solution for (dx)/(dt)=0.6-3/500 x ?
The solution for (dx)/(dt)=0.6-3/500 x is x=-(e^{-0.006t-c_{1}})/(0.006)+(0.6)/(0.006)