What is the solution for (dx)/(dt)=5-(3x)/(1000+2x) ?

The solution for (dx)/(dt)=5-(3x)/(1000+2x) is x=-(1500\W(-1/(1500e^{(49t+c_{1))/(3000)}}))/7-5000/7

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(dx)/(dt)=5-(3x)/(1000+2x)

\frac{d x}{d t} = 5 - \frac{3 x}{1000 + 2 x}

x = - \frac{1500 W ( - \frac{1}{1500 e ^{\frac{49 t + c _{1}}{3000}}} )}{7} - \frac{5000}{7}

Solution steps

\frac{d x}{d t} = 5 - \frac{3 x}{1000 + 2 x}

Solve separable ODE:

x = - \frac{1500 W ( - \frac{1}{1500 e ^{\frac{49 t + c _{1}}{3000}}} )}{7} - \frac{5000}{7}

x = - \frac{1500 W ( - \frac{1}{1500 e ^{\frac{49 t + c _{1}}{3000}}} )}{7} - \frac{5000}{7}

2 y^{^{'}} sin (t) - e^{t} y sin (t) = e^{t} y sin (t)

\frac{d y}{d t} = \frac{40}{2000} - \frac{y}{200}

y^{^{'}} + 8 y^{3} = 0

\frac{\frac{d y}{d t}}{y - 49} = - \frac{1}{5}

y^{^{'}} (s) (- s^{2} - 2 s) - 2 sy (s) = 0

What is the solution for (dx)/(dt)=5-(3x)/(1000+2x) ?
The solution for (dx)/(dt)=5-(3x)/(1000+2x) is x=-(1500\W(-1/(1500e^{(49t+c_{1))/(3000)}}))/7-5000/7