What is the solution for y^{''}+2y^'-63y=x^2 ?

The solution for y^{''}+2y^'-63y=x^2 is y=c_{1}e^{7x}+c_{2}e^{-9x}-(x^2)/(63)-(4x)/(3969)-134/250047

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y^{''}+2y^'-63y=x^2

y^{^{''}} + 2 y^{^{'}} - 63 y = x^{2}

y = c_{1} e^{7 x} + c_{2} e^{- 9 x} - \frac{x ^{2}}{63} - \frac{4 x}{3969} - \frac{134}{250047}

Solution steps

y^{''} (x) + 2 y^{'} (x) - 63 y = x^{2}

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{- 9 x} - \frac{x ^{2}}{63} - \frac{4 x}{3969} - \frac{134}{250047}

y = c_{1} e^{7 x} + c_{2} e^{- 9 x} - \frac{x ^{2}}{63} - \frac{4 x}{3969} - \frac{134}{250047}

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + y = cos (a x)

y^{^{''}} + 5 y^{^{'}} - 36 y = - 128 t + 72 t^{2}

y^{^{''}} + 4 y^{^{'}} - 32 y = - 112 t + 64 t^{2}

y^{^{''}} - 36.6 y^{^{'}} + 334.89 y = 18.5 u

What is the solution for y^{''}+2y^'-63y=x^2 ?
The solution for y^{''}+2y^'-63y=x^2 is y=c_{1}e^{7x}+c_{2}e^{-9x}-(x^2)/(63)-(4x)/(3969)-134/250047