What is the solution for (dx)/(dt)=30-x/(100) ?

The solution for (dx)/(dt)=30-x/(100) is x=-e^{(-t-c_{1})/(100)}+3000

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(dx)/(dt)=30-x/(100)

\frac{d x}{d t} = 30 - \frac{x}{100}

x = - e^{\frac{- t - c _{1}}{100}} + 3000

Solution steps

\frac{d x}{d t} = 30 - \frac{x}{100}

Solve separable ODE:

x = - e^{\frac{- t - c _{1}}{100}} + 3000

x = - e^{\frac{- t - c _{1}}{100}} + 3000

y \frac{d y}{d x} = \frac{x - e ^{x}}{e ^{y^{2}}}

\frac{d y}{d x} = \frac{20 x ^{4}}{y}

\frac{d y}{d x} = 0.2 x y

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

\frac{d y}{d x} (1 + x^{4}) - 3 x^{3} y = 0

What is the solution for (dx)/(dt)=30-x/(100) ?
The solution for (dx)/(dt)=30-x/(100) is x=-e^{(-t-c_{1})/(100)}+3000