What is the solution for (dx)/(dt)=12-9/25 x ?

The solution for (dx)/(dt)=12-9/25 x is x=-(e^{(-9t-c_{1})/(25)})/9+100/3

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(dx)/(dt)=12-9/25 x

\frac{d x}{d t} = 12 - \frac{9}{25} x

x = - \frac{e ^{\frac{- 9 t - c _{1}}{25}}}{9} + \frac{100}{3}

Solution steps

\frac{d x}{d t} = 12 - \frac{9}{25} x

Solve separable ODE:

x = - \frac{e ^{\frac{- 9 t - c _{1}}{25}}}{9} + \frac{100}{3}

x = - \frac{e ^{\frac{- 9 t - c _{1}}{25}}}{9} + \frac{100}{3}

[3 x cos (3 x) + sin (3 x) - 3] d x + (2 y + 5) d y = 0

y^{^{'}} = \frac{1 - y ^{2}}{1 - x ^{2}}

x y^{2} y^{^{'}} = x + x^{3}, y (0) = 1

y^{^{'}} = \frac{y - 1}{x + 3}

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

What is the solution for (dx)/(dt)=12-9/25 x ?
The solution for (dx)/(dt)=12-9/25 x is x=-(e^{(-9t-c_{1})/(25)})/9+100/3