What is the solution for (dx)/(dt)+(10x)/(20000-5t)=5 ?

The solution for (dx)/(dt)+(10x)/(20000-5t)=5 is x=-5(t-4000)+c_{1}(16000000-8000t+t^2)

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(dx)/(dt)+(10x)/(20000-5t)=5

\frac{d x}{d t} + \frac{10 x}{20000 - 5 t} = 5

x = - 5 (t - 4000) + c_{1} (16000000 - 8000 t + t^{2})

Solution steps

\frac{d x}{d t} + \frac{10 x}{20000 - 5 t} = 5

Solve linear ODE:

x = - 5 (t - 4000) + c_{1} (16000000 - 8000 t + t^{2})

x = - 5 (t - 4000) + c_{1} (16000000 - 8000 t + t^{2})

n = 0 \sum \infty \frac{n ^{n}}{2 ^{n}}

\int - tan (x) + 1 d x

\int (1 - x) ln (x) d x

\int \frac{sin ( 2 x )}{1 + sin ^{2} ( x )} d x

\frac{d}{d x} (2 x sin (x))

What is the solution for (dx)/(dt)+(10x)/(20000-5t)=5 ?
The solution for (dx)/(dt)+(10x)/(20000-5t)=5 is x=-5(t-4000)+c_{1}(16000000-8000t+t^2)