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Popular Calculus >

y^'=x-x^2

Solution

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

Solution

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

Solution steps

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

Popular Examples

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x \to \infty lim (- \frac{3}{x})

y^'+3(tan(3x))y=-2cos(3x)

y^{^{'}} + 3 (tan (3 x)) y = - 2 cos (3 x)

integral from 0 to 7 of (5t)/((t-8)^2)

\int_{0}^{7} \frac{5 t}{( t - 8 ) ^{2}} d t

Frequently Asked Questions (FAQ)

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