What is the solution for (dx)/(dt)=50-(7x)/(100) ?

The solution for (dx)/(dt)=50-(7x)/(100) is x=-(e^{(-7t-c_{1})/(100)})/7+5000/7

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(dx)/(dt)=50-(7x)/(100)

\frac{d x}{d t} = 50 - \frac{7 x}{100}

x = - \frac{e ^{\frac{- 7 t - c _{1}}{100}}}{7} + \frac{5000}{7}

Solution steps

\frac{d x}{d t} = 50 - \frac{7 x}{100}

Solve separable ODE:

x = - \frac{e ^{\frac{- 7 t - c _{1}}{100}}}{7} + \frac{5000}{7}

x = - \frac{e ^{\frac{- 7 t - c _{1}}{100}}}{7} + \frac{5000}{7}

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

\frac{d y}{d x} = \frac{sec ( y )}{csc ( x )}, y = \frac{π}{4}

(- y) d x + (x) d y = 0

y^{^{'}} + \frac{1}{2} y = 9

y^{2} \frac{d y}{d x} - cos (x) = 0

What is the solution for (dx)/(dt)=50-(7x)/(100) ?
The solution for (dx)/(dt)=50-(7x)/(100) is x=-(e^{(-7t-c_{1})/(100)})/7+5000/7