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

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

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

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} - x^{2} + \frac{x}{2} - \frac{3}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} - x^{2} + \frac{x}{2} - \frac{3}{4}

y = c_{1} e^{x} + c_{2} e^{- 2 x} - x^{2} + \frac{x}{2} - \frac{3}{4}

y^{^{''}} - 25 y = e^{5 t}

y^{^{''}} + 12 y = 7 e^{2 x}

y^{^{''}} - 14 y^{^{'}} + 49 y = (x + 1) e^{x}

y^{^{''}} - 10 y^{^{'}} + 25 y = 4 e^{5 x}

y^{^{''}} + 10 y^{^{'}} + 25 y = 50 sin (5 x)

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