What is the solution for (dx)/(dt)=0.075x-9000 ?

The solution for (dx)/(dt)=0.075x-9000 is x=(e^{0.075t+c_{1}})/(0.075)+(9000)/(0.075)

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(dx)/(dt)=0.075x-9000

\frac{d x}{d t} = 0.075 x - 9000

x = \frac{e ^{0.075 t + c_{1}}}{0.075} + \frac{9000}{0.075}

Solution steps

\frac{d x}{d t} = 0.075 x - 9000

Solve separable ODE:

x = \frac{e ^{0.075 t + c_{1}}}{0.075} + \frac{9000}{0.075}

x = \frac{e ^{0.075 t + c_{1}}}{0.075} + \frac{9000}{0.075}

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

\frac{d y}{d x} = \frac{- 3 x + 3 x y ^{2}}{y x ^{2} + 2 y}

\frac{d y}{d x} = x y + x - 2 y - 2

\frac{d y}{d x} = - \frac{7 sin ( 3 x )}{2 y}

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

What is the solution for (dx)/(dt)=0.075x-9000 ?
The solution for (dx)/(dt)=0.075x-9000 is x=(e^{0.075t+c_{1}})/(0.075)+(9000)/(0.075)