What is the solution for (dy)/(dx)=0.2(4000-y) ?

The solution for (dy)/(dx)=0.2(4000-y) is y=-e^{-x/5-c_{1}}+4000

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(dy)/(dx)=0.2(4000-y)

\frac{d y}{d x} = 0.2 (4000 - y)

y = - e^{- \frac{x}{5} - c_{1}} + 4000

Solution steps

\frac{d y}{d x} = 0.2 (4000 - y)

Solve separable ODE:

y = - e^{- \frac{x}{5} - c_{1}} + 4000

y = - e^{- \frac{x}{5} - c_{1}} + 4000

\frac{\partial}{\partial x} (\frac{x y}{1 + x ^{2} + y ^{2}})

\frac{d}{d x} (cos^{2} (2 x) - x^{2})

\frac{\partial}{\partial x} (cos (3 x + 4 y))

x \to 1 lim (3 - 2 x)

What is the solution for (dy)/(dx)=0.2(4000-y) ?
The solution for (dy)/(dx)=0.2(4000-y) is y=-e^{-x/5-c_{1}}+4000