What is the solution for y^{''}-y^'-2y=2x^3-3x^2+8x+1 ?

The solution for y^{''}-y^'-2y=2x^3-3x^2+8x+1 is y=c_{1}e^{2x}+c_{2}e^{-x}-x^3+3x^2-10x+15/2

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y^{''}-y^'-2y=2x^3-3x^2+8x+1

y^{^{''}} - y^{^{'}} - 2 y = 2 x^{3} - 3 x^{2} + 8 x + 1

y = c_{1} e^{2 x} + c_{2} e^{- x} - x^{3} + 3 x^{2} - 10 x + \frac{15}{2}

Solution steps

y^{''} (x) - y^{'} (x) - 2 y = 2 x^{3} - 3 x^{2} + 8 x + 1

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - x^{3} + 3 x^{2} - 10 x + \frac{15}{2}

y = c_{1} e^{2 x} + c_{2} e^{- x} - x^{3} + 3 x^{2} - 10 x + \frac{15}{2}

y^{^{''}} + 16 y = 8 e^{3 x}

y^{^{''}} + 4 y = x - \frac{x ^{2}}{20}

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

y^{^{''}} + 4 y = sin (x), y^{^{'}} (π) = 0, y (0) = 0

y^{^{'''}} - 19 y^{^{'}} + 30 y = x^{2} e^{2 x}

What is the solution for y^{''}-y^'-2y=2x^3-3x^2+8x+1 ?
The solution for y^{''}-y^'-2y=2x^3-3x^2+8x+1 is y=c_{1}e^{2x}+c_{2}e^{-x}-x^3+3x^2-10x+15/2