What is the solution for y^{''}-y=4x^2-1 ?

The solution for y^{''}-y=4x^2-1 is y=c_{1}e^x+c_{2}e^{-x}-4x^2-7

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y^{''}-y=4x^2-1

y^{^{''}} - y = 4 x^{2} - 1

y = c_{1} e^{x} + c_{2} e^{- x} - 4 x^{2} - 7

Solution steps

y^{''} (x) - y = 4 x^{2} - 1

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - 4 x^{2} - 7

y = c_{1} e^{x} + c_{2} e^{- x} - 4 x^{2} - 7

2 y^{^{''}} + 8 y^{^{'}} + 8 y = e^{- 2 x} + x

y^{^{''}} - 4 y^{^{'}} + 4 y = 3 e^{2 x} + x sin (x)

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

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- x} + 3 e^{x}

(d^{2} - 3 d) y = x^{2} + 2 x - 6

What is the solution for y^{''}-y=4x^2-1 ?
The solution for y^{''}-y=4x^2-1 is y=c_{1}e^x+c_{2}e^{-x}-4x^2-7