What is the solution for (dx)/(dt)=6-(3x)/(500),x(0)=0 ?

The solution for (dx)/(dt)=6-(3x)/(500),x(0)=0 is x=-1000e^{-(3t)/(500)}+1000

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(dx)/(dt)=6-(3x)/(500),x(0)=0

\frac{d x}{d t} = 6 - \frac{3 x}{500}, x (0) = 0

x = - 1000 e^{- \frac{3 t}{500}} + 1000

Solution steps

\frac{d x}{d t} = 6 - \frac{3 x}{500}

Solve separable ODE:

x = - 1000 e^{- \frac{3 t}{500}} + 1000

x = - 1000 e^{- \frac{3 t}{500}} + 1000

\frac{x}{x ^{2} + 1}

f (x) = x^{2} - 1, at x = - 1

\frac{6}{( s ^{2} + 9 ) ^{2}}

x \to 2 + lim (\frac{7}{x - 2})

What is the solution for (dx)/(dt)=6-(3x)/(500),x(0)=0 ?
The solution for (dx)/(dt)=6-(3x)/(500),x(0)=0 is x=-1000e^{-(3t)/(500)}+1000