What is the solution for (dy)/(dx)=5(1-x/(10)) ?

The solution for (dy)/(dx)=5(1-x/(10)) is y=5(x-(x^2)/(20))+c_{1}

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(dy)/(dx)=5(1-x/(10))

\frac{d y}{d x} = 5 (1 - \frac{x}{10})

y = 5 (x - \frac{x ^{2}}{20}) + c_{1}

Solution steps

\frac{d y}{d x} = 5 (1 - \frac{x}{10})

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 5 (1 - \frac{x}{10})

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

then

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

y = \int 5 (1 - \frac{x}{10}) d x

\int 5 (1 - \frac{x}{10}) d x = 5 (x - \frac{x ^{2}}{20}) + c_{1}

y = 5 (x - \frac{x ^{2}}{20}) + c_{1}

\int_{- 2}^{0} - x + 2 d x

\int - 20 x^{- 5} d x

\frac{d y}{d x} = e^{y - x}

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

\frac{d ^{2}}{d x ^{2}} (x ln (x))

What is the solution for (dy)/(dx)=5(1-x/(10)) ?
The solution for (dy)/(dx)=5(1-x/(10)) is y=5(x-(x^2)/(20))+c_{1}