What is the solution for (dx)/(dt)-0.04x=5000 ?

The solution for (dx)/(dt)-0.04x=5000 is x=25e^{(t+c_{1})/(25)}-125000

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(dx)/(dt)-0.04x=5000

\frac{d x}{d t} - 0.04 x = 5000

x = 25 e^{\frac{t + c _{1}}{25}} - 125000

Solution steps

\frac{d x}{d t} - 0.04 x = 5000

Solve separable ODE:

x = 25 e^{\frac{t + c _{1}}{25}} - 125000

x = 25 e^{\frac{t + c _{1}}{25}} - 125000

d y (x y - 2 x + 4 y - 8) - d x (x y + 3 x - y - 3) = 0

(4 y - 5) d x + (7 x - 2) d y = 0

y^{^{'}} + y^{2} - y = 0

(6 y^{2} + 4 x y^{3}) d x + (6 x y + 4 x^{2} y^{2}) d y = 0

\frac{d y}{d x} = 600 y

What is the solution for (dx)/(dt)-0.04x=5000 ?
The solution for (dx)/(dt)-0.04x=5000 is x=25e^{(t+c_{1})/(25)}-125000