What is the solution for (dx)/(dt)=-9000+(7.5)/(100)x ?

The solution for (dx)/(dt)=-9000+(7.5)/(100)x is x=-(e^{0.075t+c_{1}})/(7.5)+(900000)/(7.5)

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(dx)/(dt)=-9000+(7.5)/(100)x

\frac{d x}{d t} = - 9000 + \frac{7.5}{100} x

x = - \frac{e ^{0.075 t + c_{1}}}{7.5} + \frac{900000}{7.5}

Solution steps

\frac{d x}{d t} = - 9000 + \frac{7.5}{100} x

Solve separable ODE:

x = - \frac{e ^{0.075 t + c_{1}}}{7.5} + \frac{900000}{7.5}

x = - \frac{e ^{0.075 t + c_{1}}}{7.5} + \frac{900000}{7.5}

2 y y^{^{'}} = 9 t^{2}, y (0) = 2

x^{^{'}} = a + b \cdot x

sin (x) y^{^{'}} + \frac{sin ^{2} ( x )}{cos ( x )} y = 0

y^{^{'}} = - \frac{1}{5} y^{2}, y (0) = 0.25

4 \frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

What is the solution for (dx)/(dt)=-9000+(7.5)/(100)x ?
The solution for (dx)/(dt)=-9000+(7.5)/(100)x is x=-(e^{0.075t+c_{1}})/(7.5)+(900000)/(7.5)