What is the solution for y^{''}-4y=8x^2-2x ?

The solution for y^{''}-4y=8x^2-2x is y=c_{1}e^{2x}+c_{2}e^{-2x}-2x^2+x/2-1

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y^{''}-4y=8x^2-2x

y^{^{''}} - 4 y = 8 x^{2} - 2 x

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

Solution steps

y^{''} (x) - 4 y = 8 x^{2} - 2 x

Solve linear ODE:

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

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

y^{^{''}} + 9 y = 1

u^{^{''}} - a \cdot H (x) = x, u^{^{'}} (- 1) = 0, u^{^{'}} (1) = 0

y^{^{''}} + 4 y = e^{3 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + a^{2} y = cos (b t)

y^{^{''}} - 12 y^{^{'}} + 36 y = 7 + 2 x

What is the solution for y^{''}-4y=8x^2-2x ?
The solution for y^{''}-4y=8x^2-2x is y=c_{1}e^{2x}+c_{2}e^{-2x}-2x^2+x/2-1