What is the solution for y^{''}-4y=6x-4x^3 ?

The solution for y^{''}-4y=6x-4x^3 is y=c_{1}e^{2x}+c_{2}e^{-2x}+x^3

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y^{''}-4y=6x-4x^3

y^{^{''}} - 4 y = 6 x - 4 x^{3}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + x^{3}

Solution steps

y^{''} (x) - 4 y = 6 x - 4 x^{3}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + x^{3}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + x^{3}

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} - 4 y = - 3 e^{t} + 4 e^{2 t}

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 + 16 x

y^{^{''}} + y = 2 x \cdot sin (x)

2 y^{^{''}} - 4 y^{^{'}} + 3 y = 2 e^{3 x} - 6

y^{^{''}} - 5 y = (x - 1) sin (x) + (x + 1) cos (x)

What is the solution for y^{''}-4y=6x-4x^3 ?
The solution for y^{''}-4y=6x-4x^3 is y=c_{1}e^{2x}+c_{2}e^{-2x}+x^3