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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 4} e^{4 t}

\int_{1}^{2} 5 x^{2} ln (x) d x

f (x) = 6 x^{\frac{1}{2}}

y = 12 x^{2} - 7 x - 2 x^{- 2}

\int \frac{cos ^{3} ( x )}{sin ( x )} d x

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