What is the solution for (dx)/(dt)=0.6-(5x)/(1000+t) ?

The solution for (dx)/(dt)=0.6-(5x)/(1000+t) is

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(dx)/(dt)=0.6-(5x)/(1000+t)

\frac{d x}{d t} = 0.6 - \frac{5 x}{1000 + t}

x = \frac{0.6 ( 1.0 E 15 t + 2500000000000 t ^{2} + 3333333333.33333 \dots t ^{3} + 2500000 t ^{4} + 1000 t ^{5} + 0.16666 \dots t ^{6} )}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}} + \frac{c _{1}}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}}

Solution steps

\frac{d x}{d t} = 0.6 - \frac{5 x}{1000 + t}

Solve linear ODE:

x = \frac{0.6 ( 1.0 E 15 t + 2500000000000 t ^{2} + 3333333333.33333 \dots t ^{3} + 2500000 t ^{4} + 1000 t ^{5} + 0.16666 \dots t ^{6} )}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}} + \frac{c _{1}}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}}

x = \frac{0.6 ( 1.0 E 15 t + 2500000000000 t ^{2} + 3333333333.33333 \dots t ^{3} + 2500000 t ^{4} + 1000 t ^{5} + 0.16666 \dots t ^{6} )}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}} + \frac{c _{1}}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}}

y = ln (x + 4)

x \to 0 lim (∣ e^{x} - 1 ∣)

\int 1 + 9 x d x

x y^{^{''}} + 2 y^{^{'}} = 16 x^{2}

\int_{0}^{N} e^{(- s t)} e^{- 5 t} d t

What is the solution for (dx)/(dt)=0.6-(5x)/(1000+t) ?
The solution for (dx)/(dt)=0.6-(5x)/(1000+t) is