What is the solution for dx=6*0.5-6*x/(50)dt ?

The solution for dx=6*0.5-6*x/(50)dt is x=-(e^{(-3t-c_{1})/(25)})/3+25

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dx=60.5-6x/(50)dt

d x = 6 \cdot 0.5 - 6 \cdot \frac{x}{50} d t

x = - \frac{e ^{\frac{- 3 t - c _{1}}{25}}}{3} + 25

Solution steps

d x = 6 \cdot 0.5 - 6 \cdot \frac{x}{50} d t

Solve separable ODE:

x = - \frac{e ^{\frac{- 3 t - c _{1}}{25}}}{3} + 25

x = - \frac{e ^{\frac{- 3 t - c _{1}}{25}}}{3} + 25

\frac{d y}{d t} = 0.07 (100 - y), y (0) = 25

y - 9 \frac{d y}{d t} = 0

\frac{d y}{d x} y = u, u = x^{2} + 2

\frac{d y}{d t} = 3 y, y (6) = 1

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

What is the solution for dx=6*0.5-6*x/(50)dt ?
The solution for dx=6*0.5-6*x/(50)dt is x=-(e^{(-3t-c_{1})/(25)})/3+25