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

The solution for y^{''}-5y=x^2-2x is y=c_{1}e^{sqrt(5)x}+c_{2}e^{-sqrt(5)x}-(x^2)/5+(2x)/5-2/25

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

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

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{x ^{2}}{5} + \frac{2 x}{5} - \frac{2}{25}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{x ^{2}}{5} + \frac{2 x}{5} - \frac{2}{25}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{x ^{2}}{5} + \frac{2 x}{5} - \frac{2}{25}

y^{^{''}} - 3 y^{^{'}} - 4 y = 2 e^{- t}

y^{^{''}} + 8 y^{^{'}} + 2 y = cos (x), y (0) = 0, y^{^{'}} (0) = 1

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 x + 6

y^{^{''}} + y^{^{'}} - 6 y = x e^{2 x}

What is the solution for y^{''}-5y=x^2-2x ?
The solution for y^{''}-5y=x^2-2x is y=c_{1}e^{sqrt(5)x}+c_{2}e^{-sqrt(5)x}-(x^2)/5+(2x)/5-2/25