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

The solution for 2y^{''}-y^'-3y=3xe^{2x} is y=c_{1}e^{(3x)/2}+c_{2}e^{-x}+e^{2x}x-7/3 e^{2x}

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

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

y = c_{1} e^{\frac{3 x}{2}} + c_{2} e^{- x} + e^{2 x} x - \frac{7}{3} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{3 x}{2}} + c_{2} e^{- x} + e^{2 x} x - \frac{7}{3} e^{2 x}

y = c_{1} e^{\frac{3 x}{2}} + c_{2} e^{- x} + e^{2 x} x - \frac{7}{3} e^{2 x}

y^{^{''}} + y = x^{2} + 1, y (0) = 3, y (1) = 0

D (D + 3) y = x (5 + e^{x})

y^{^{''}} + 2 y^{^{'}} - 3 y = 4 e^{2 t}

y^{^{''}} - y = e^{t} cos (t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y = 1, y (0) = 2, y^{^{'}} (0) = 1

What is the solution for 2y^{''}-y^'-3y=3xe^{2x} ?
The solution for 2y^{''}-y^'-3y=3xe^{2x} is y=c_{1}e^{(3x)/2}+c_{2}e^{-x}+e^{2x}x-7/3 e^{2x}