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Popular >

x^3y^'+2x^2y=2cos(3x)y^{-1/2}

Solution

x^{3} y^{^{'}} + 2 x^{2} y = 2 cos (3 x) y^{- \frac{1}{2}}

Solution

y = \frac{( sin ^{2} ( 3 x ) + 2 c _{1} sin ( 3 x ) + c _{1}^{2} ) ^{\frac{1}{3}}}{x ^{2}}

Solution steps

x^{3} y^{'} (x) + 2 x^{2} y = 2 cos (3 x) y^{- \frac{1}{2}}

Solve Bernoulli ODE:

y = \frac{( sin ^{2} ( 3 x ) + 2 c _{1} sin ( 3 x ) + c _{1}^{2} ) ^{\frac{1}{3}}}{x ^{2}}

y = \frac{( sin ^{2} ( 3 x ) + 2 c _{1} sin ( 3 x ) + c _{1}^{2} ) ^{\frac{1}{3}}}{x ^{2}}

Graph

Popular Examples

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x \to \infty lim (\frac{2 x ^{2} - 9 x - 2}{- 5 x ^{2} - 10 x + 3})

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

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\frac{d}{d x} (\frac{e ^{7 x} + e ^{- 7 x}}{x})

integral from 0 to 1 of-x^2

\int_{0}^{1} - x^{2} d x

Frequently Asked Questions (FAQ)

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