What is the solution for y^{''}-3y^'+5y=4x^3-2x ?

The solution for y^{''}-3y^'+5y=4x^3-2x is

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y^{''}-3y^'+5y=4x^3-2x

y^{^{''}} - 3 y^{^{'}} + 5 y = 4 x^{3} - 2 x

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{11 x}{2}) + c_{2} sin (\frac{11 x}{2})) + \frac{4 x ^{3}}{5} + \frac{36 x ^{2}}{25} + \frac{46 x}{125} - \frac{222}{625}

Solution steps

y^{''} (x) - 3 y^{'} (x) + 5 y = 4 x^{3} - 2 x

Solve linear ODE:

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{11 x}{2}) + c_{2} sin (\frac{11 x}{2})) + \frac{4 x ^{3}}{5} + \frac{36 x ^{2}}{25} + \frac{46 x}{125} - \frac{222}{625}

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{11 x}{2}) + c_{2} sin (\frac{11 x}{2})) + \frac{4 x ^{3}}{5} + \frac{36 x ^{2}}{25} + \frac{46 x}{125} - \frac{222}{625}

y^{^{''}} - 8 y^{^{'}} + 16 y = 24 x + 2, y (0) = 2, y^{^{'}} (0) = - 1

y^{^{'''}} + y^{^{''}} - 5 y^{^{'}} + 3 y = e^{- t} + sin (t)

y^{^{''}} - y^{^{'}} + 100 y = 10 sin (10 t)

\frac{d ^{2} y}{d x ^{2}} + 100 y = 1000 sin (10 x)

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 3 + x^{- 1} e^{x}

What is the solution for y^{''}-3y^'+5y=4x^3-2x ?
The solution for y^{''}-3y^'+5y=4x^3-2x is