What is the solution for (d^2y)/(dx^2)-4y=8x^2-x+12 ?

The solution for (d^2y)/(dx^2)-4y=8x^2-x+12 is y=c_{1}e^{2x}+c_{2}e^{-2x}-2x^2+x/4-4

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(d^2y)/(dx^2)-4y=8x^2-x+12

\frac{d ^{2} y}{d x ^{2}} - 4 y = 8 x^{2} - x + 12

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - 2 x^{2} + \frac{x}{4} - 4

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 y = 8 x^{2} - x + 12

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - 2 x^{2} + \frac{x}{4} - 4

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - 2 x^{2} + \frac{x}{4} - 4

y^{^{'''}} + 5 y^{^{''}} - 14 = 0

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

x^{^{''}} - 6 x^{^{'}} + 9 x = e^{3 t}

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

y^{^{''}} + 100 y^{^{'}} + 2500 y = 30, y (0) = 0, y^{^{'}} (0) = 2

What is the solution for (d^2y)/(dx^2)-4y=8x^2-x+12 ?
The solution for (d^2y)/(dx^2)-4y=8x^2-x+12 is y=c_{1}e^{2x}+c_{2}e^{-2x}-2x^2+x/4-4