What is the solution for y^{''}-2y^'=12x^2 ?

The solution for y^{''}-2y^'=12x^2 is y=c_{1}e^{2x}+c_{2}-2x^3-3x^2-3x

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y^{''}-2y^'=12x^2

y^{^{''}} - 2 y^{^{'}} = 12 x^{2}

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

Solution steps

y^{''} (x) - 2 y^{'} (x) = 12 x^{2}

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 5 x^{- 2 x}

y^{^{''}} - 3 y^{^{'}} - 5 = e^{2 x} - 3 cos (3 x)

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

y^{^{''}} + 10 y^{^{'}} + 16 y = 949 sin (3 t)

y^{^{''}} + 2 y^{^{'}} + 5 y = 10 cos (x)

What is the solution for y^{''}-2y^'=12x^2 ?
The solution for y^{''}-2y^'=12x^2 is y=c_{1}e^{2x}+c_{2}-2x^3-3x^2-3x