What is the solution for y^'-2y=-5x^2 ?

The solution for y^'-2y=-5x^2 is y=-(5e^{2x}(-2e^{-2x}x^2-2e^{-2x}x-e^{-2x}))/4+c_{1}e^{2x}

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y^'-2y=-5x^2

y^{^{'}} - 2 y = - 5 x^{2}

y = - \frac{5 e ^{2 x} ( - 2 e ^{- 2 x} x ^{2} - 2 e ^{- 2 x} x - e ^{- 2 x} )}{4} + c_{1} e^{2 x}

Solution steps

y^{'} (x) - 2 y = - 5 x^{2}

Solve linear ODE:

y = - \frac{5 e ^{2 x} ( - 2 e ^{- 2 x} x ^{2} - 2 e ^{- 2 x} x - e ^{- 2 x} )}{4} + c_{1} e^{2 x}

y = - \frac{5 e ^{2 x} ( - 2 e ^{- 2 x} x ^{2} - 2 e ^{- 2 x} x - e ^{- 2 x} )}{4} + c_{1} e^{2 x}

f (x) = 3 e^{- 4 x}, at x = 0

\frac{s}{s ^{2} - 2 s + 10}

\frac{d}{d x} (\frac{6 x ^{2} + 4 x + 2}{x})

\frac{d}{d y} (\frac{y ^{4} + 48}{24 y})

\int \frac{x ^{3} - 1}{x ^{4} - 4 x} d x

What is the solution for y^'-2y=-5x^2 ?
The solution for y^'-2y=-5x^2 is y=-(5e^{2x}(-2e^{-2x}x^2-2e^{-2x}x-e^{-2x}))/4+c_{1}e^{2x}