What is the solution for y^{''}+7y^'+10y=3x^2+x-2 ?

The solution for y^{''}+7y^'+10y=3x^2+x-2 is y=c_{1}e^{-2x}+c_{2}e^{-5x}+(3x^2)/(10)-(8x)/(25)-9/250

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y^{''}+7y^'+10y=3x^2+x-2

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 x^{2} + x - 2

y = c_{1} e^{- 2 x} + c_{2} e^{- 5 x} + \frac{3 x ^{2}}{10} - \frac{8 x}{25} - \frac{9}{250}

Solution steps

y^{''} (x) + 7 y^{'} (x) + 10 y = 3 x^{2} + x - 2

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 5 x} + \frac{3 x ^{2}}{10} - \frac{8 x}{25} - \frac{9}{250}

y = c_{1} e^{- 2 x} + c_{2} e^{- 5 x} + \frac{3 x ^{2}}{10} - \frac{8 x}{25} - \frac{9}{250}

y^{^{''}} - 4 y = 8 x^{3}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + a y^{^{'}} + b y = sin (x) + 1

y^{^{''}} - y^{^{'}} - 6 y = 5 cos (3 x)

y^{^{''}} - 18 y^{^{'}} + 81 y = t^{9} e^{9 t}

y^{^{''}} - y^{^{'}} = 3 - 4 x, y (0) = - 3, y^{^{'}} (0) = 0

What is the solution for y^{''}+7y^'+10y=3x^2+x-2 ?
The solution for y^{''}+7y^'+10y=3x^2+x-2 is y=c_{1}e^{-2x}+c_{2}e^{-5x}+(3x^2)/(10)-(8x)/(25)-9/250