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Popular Calculus >

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

Solution

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

Solution

y = \frac{x ^{2}}{2} - \frac{x ^{3}}{3} + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x - x^{2}

If

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

then

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

y = \int x - x^{2} d x

\int x - x^{2} d x = \frac{x ^{2}}{2} - \frac{x ^{3}}{3} + c_{1}

y = \frac{x ^{2}}{2} - \frac{x ^{3}}{3} + c_{1}

Graph

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d er i v a t i v e f (x) = sin (x) + cos (x)

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d er i v a t i v e A e^{- 4}

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\int \frac{x}{x ^{2} + x - 6} d x

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in v erse l a pl a ce \frac{2}{3 ( s + 1 ) ^{2} - 27}

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=x-x^2 ?
The solution for (dy)/(dx)=x-x^2 is y=(x^2)/2-(x^3)/3+c_{1}