What is the solution for (dy)/(dx)=2-(2x)/(1000-x) ?

The solution for (dy)/(dx)=2-(2x)/(1000-x) is y=4x+2000ln(-x+1000)-2000+c_{1}

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(dy)/(dx)=2-(2x)/(1000-x)

\frac{d y}{d x} = 2 - \frac{2 x}{1000 - x}

y = 4 x + 2000 ln (- x + 1000) - 2000 + c_{1}

Solution steps

\frac{d y}{d x} = 2 - \frac{2 x}{1000 - x}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 2 - \frac{2 x}{1000 - x}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int 2 - \frac{2 x}{1000 - x} d x

\int 2 - \frac{2 x}{1000 - x} d x = 4 x + 2000 ln (- x + 1000) - 2000 + c_{1}

y = 4 x + 2000 ln (- x + 1000) - 2000 + c_{1}

\frac{d}{d x} (x coth (1 + x^{2}))

y = ln (1 + e^{x})

\frac{\partial}{\partial x} (sin (5 x - 8 y))

e^{x}, e^{- 3 x}, x = ln (3)

\int \frac{9 x + 6}{( x - 6 ) ( x + 4 )} d x

What is the solution for (dy)/(dx)=2-(2x)/(1000-x) ?
The solution for (dy)/(dx)=2-(2x)/(1000-x) is y=4x+2000ln(-x+1000)-2000+c_{1}