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Popular Calculus >

xy^'+3y=x^3-x

Solution

x y^{^{'}} + 3 y = x^{3} - x

Solution

y = \frac{x ^{3}}{6} - \frac{x}{4} + \frac{c _{1}}{x ^{3}}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{3}}{6} - \frac{x}{4} + \frac{c _{1}}{x ^{3}}

y = \frac{x ^{3}}{6} - \frac{x}{4} + \frac{c _{1}}{x ^{3}}

Graph

Popular Examples

integral of sin^9(x)cos^3(x)

\int sin^{9} (x) cos^{3} (x) d x

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d er i v a t i v e y = \frac{7 x - 24}{x ^{2} + 2 x}

integral of 1/(3x^6)

\int \frac{1}{3 x ^{6}} d x

derivative of ln((e^x/x))

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

derivative of 5x^6

\frac{d}{d x} (5 x^{6})

Frequently Asked Questions (FAQ)

What is the solution for xy^'+3y=x^3-x ?
The solution for xy^'+3y=x^3-x is y=(x^3)/6-x/4+(c_{1})/(x^3)