What is the solution for (dx)/(dt)=20-0.4x ?

The solution for (dx)/(dt)=20-0.4x is x=-(5e^{(-2t-c_{1})/5})/(2)+50

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(dx)/(dt)=20-0.4x

\frac{d x}{d t} = 20 - 0.4 x

x = - \frac{5 e ^{\frac{- 2 t - c _{1}}{5}}}{2} + 50

Solution steps

\frac{d x}{d t} = 20 - 0.4 x

Solve separable ODE:

x = - \frac{5 e ^{\frac{- 2 t - c _{1}}{5}}}{2} + 50

x = - \frac{5 e ^{\frac{- 2 t - c _{1}}{5}}}{2} + 50

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

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

\frac{d y}{d x} = y^{2} + 1, y (0) = 0

\frac{d p}{d t} = 2 pt, p (1) = 6

y^{^{'}} + 3 y = 13, y (0) = 0

What is the solution for (dx)/(dt)=20-0.4x ?
The solution for (dx)/(dt)=20-0.4x is x=-(5e^{(-2t-c_{1})/5})/(2)+50