What is the solution for y^{''}-7y^'-8y=8x^2-2x ?

The solution for y^{''}-7y^'-8y=8x^2-2x is y=c_{1}e^{8x}+c_{2}e^{-x}-x^2+2x-2

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y^{''}-7y^'-8y=8x^2-2x

y^{^{''}} - 7 y^{^{'}} - 8 y = 8 x^{2} - 2 x

y = c_{1} e^{8 x} + c_{2} e^{- x} - x^{2} + 2 x - 2

Solution steps

y^{''} (x) - 7 y^{'} (x) - 8 y = 8 x^{2} - 2 x

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} e^{- x} - x^{2} + 2 x - 2

y = c_{1} e^{8 x} + c_{2} e^{- x} - x^{2} + 2 x - 2

x^{^{''}} + 4 x^{^{'}} + 16 x = 4 sin (2 t)

y^{^{''}} + 16 y = cos (4 t), y (0) = 3, y^{^{'}} (0) = 2

y^{^{''}} - 5 y^{^{'}} - 6 y = 10

3 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 25 y = cos (2 x)

y^{^{'''}} + 3 y^{^{'}} - 2 x = 0

What is the solution for y^{''}-7y^'-8y=8x^2-2x ?
The solution for y^{''}-7y^'-8y=8x^2-2x is y=c_{1}e^{8x}+c_{2}e^{-x}-x^2+2x-2