What is the solution for (dx)/(dt)=4000-x/(50+t) ?

The solution for (dx)/(dt)=4000-x/(50+t) is x=(2000(t^2+100t))/(50+t)+(c_{1})/(50+t)

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(dx)/(dt)=4000-x/(50+t)

\frac{d x}{d t} = 4000 - \frac{x}{50 + t}

x = \frac{2000 ( t ^{2} + 100 t )}{50 + t} + \frac{c _{1}}{50 + t}

Solution steps

\frac{d x}{d t} = 4000 - \frac{x}{50 + t}

Solve linear ODE:

x = \frac{2000 ( t ^{2} + 100 t )}{50 + t} + \frac{c _{1}}{50 + t}

x = \frac{2000 ( t ^{2} + 100 t )}{50 + t} + \frac{c _{1}}{50 + t}

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

n = 1 \sum \infty \frac{( - 1 ) ^{n}}{n ( n ^{2} + 1 ) ^{\frac{1}{2}}}

\frac{\partial}{\partial x} (- x y z^{2} + 27)

\frac{d}{d x} (ln (x^{2} - 9 x + 1))

n = 0 \sum \infty \frac{n ^{10} \cdot 1 0 ^{n}}{n !}

What is the solution for (dx)/(dt)=4000-x/(50+t) ?
The solution for (dx)/(dt)=4000-x/(50+t) is x=(2000(t^2+100t))/(50+t)+(c_{1})/(50+t)