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}

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)