What is the solution for (dx)/(dt)=14-0.28*x ?

The solution for (dx)/(dt)=14-0.28*x is x=-(e^{-0.28t-c_{1}})/(0.28)+(14)/(0.28)

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(dx)/(dt)=14-0.28*x

\frac{d x}{d t} = 14 - 0.28 \cdot x

x = - \frac{e ^{- 0.28 t - c_{1}}}{0.28} + \frac{14}{0.28}

Solution steps

\frac{d x}{d t} = 14 - 0.28 \cdot x

Solve separable ODE:

x = - \frac{e ^{- 0.28 t - c_{1}}}{0.28} + \frac{14}{0.28}

x = - \frac{e ^{- 0.28 t - c_{1}}}{0.28} + \frac{14}{0.28}

\frac{d x}{d t} = \frac{8 \cdot 1 0 ^{- 3}}{100} - 8 \frac{x}{9500}

\frac{d y}{d t} = \frac{3 t ^{2}}{8 y}

y^{^{'}} = (8 x - 5) (y + 2)

(e^{y} + 1)^{2} e^{- y} d x + (e^{x} + 1)^{2} e^{- x} d y = 0

(y^{2} + y) d x - (x^{2} + x) d y = 0

What is the solution for (dx)/(dt)=14-0.28*x ?
The solution for (dx)/(dt)=14-0.28*x is x=-(e^{-0.28t-c_{1}})/(0.28)+(14)/(0.28)