What is the solution for (dx)/(dt)=37.5-3.5x ?

The solution for (dx)/(dt)=37.5-3.5x is x=-(e^{-3.49999…t-c_{1}})/(3.5)+(37.5)/(3.5)

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(dx)/(dt)=37.5-3.5x

\frac{d x}{d t} = 37.5 - 3.5 x

x = - \frac{e ^{- 3.49999 \dots t - c_{1}}}{3.5} + \frac{37.5}{3.5}

Solution steps

\frac{d x}{d t} = 37.5 - 3.5 x

Solve separable ODE:

x = - \frac{e ^{- 3.49999 \dots t - c_{1}}}{3.5} + \frac{37.5}{3.5}

x = - \frac{e ^{- 3.49999 \dots t - c_{1}}}{3.5} + \frac{37.5}{3.5}

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

\frac{d y}{d x} = \frac{4 x + x y ^{2}}{2 y + x ^{2} y}

(2 x + 1) d x + (5 - 6 y) d y = 0

y^{^{'}} = 12 y^{- 2}, y (0) = 3

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

What is the solution for (dx)/(dt)=37.5-3.5x ?
The solution for (dx)/(dt)=37.5-3.5x is x=-(e^{-3.49999…t-c_{1}})/(3.5)+(37.5)/(3.5)