What is the solution for y^{''}-2y^'-3y=6xe^x+4x-5 ?

The solution for y^{''}-2y^'-3y=6xe^x+4x-5 is y=c_{1}e^{3x}+c_{2}e^{-x}-(3e^xx)/2-(4x)/3+23/9

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y^{''}-2y^'-3y=6xe^x+4x-5

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x e^{x} + 4 x - 5

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{3 e ^{x} x}{2} - \frac{4 x}{3} + \frac{23}{9}

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 6 x e^{x} + 4 x - 5

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{3 e ^{x} x}{2} - \frac{4 x}{3} + \frac{23}{9}

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{3 e ^{x} x}{2} - \frac{4 x}{3} + \frac{23}{9}

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

y^{^{''}} + 3 y = 5 t^{4}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 10 y^{^{'}} + 24 = 0

y^{^{'''}} + 3 y^{^{''}} - 4 = 0

2 y^{^{''}} + 8 y^{^{'}} - y = 8

What is the solution for y^{''}-2y^'-3y=6xe^x+4x-5 ?
The solution for y^{''}-2y^'-3y=6xe^x+4x-5 is y=c_{1}e^{3x}+c_{2}e^{-x}-(3e^xx)/2-(4x)/3+23/9