What is the solution for (df)/(dx)=1-(r)f(x) ?

The solution for (df)/(dx)=1-(r)f(x) is f(x)=-(e^{-rx-c_{1}r})/r+1/r

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(df)/(dx)=1-(r)f(x)

\frac{df}{d x} = 1 - (r) f (x)

f (x) = - \frac{e ^{- r x - c_{1} r}}{r} + \frac{1}{r}

Solution steps

\frac{df}{d x} = 1 - (r) f

Solve separable ODE:

f (x) = - \frac{e ^{- r x - c_{1} r}}{r} + \frac{1}{r}

f (x) = - \frac{e ^{- r x - c_{1} r}}{r} + \frac{1}{r}

\frac{d z}{d t} = 6 t e^{4 z}

y^{^{'}} - 5 y = 8, e^{5 x} y (0) = 0

\frac{d x}{d t} = 2 x x

8 x \frac{d y}{d x} = - \frac{1}{y ^{3} 1 + x}

\frac{d y}{d t} + e^{t} y = 24 e^{t}

What is the solution for (df)/(dx)=1-(r)f(x) ?
The solution for (df)/(dx)=1-(r)f(x) is f(x)=-(e^{-rx-c_{1}r})/r+1/r