What is the solution for (D^2-5D+6)y=3e^{3x}+e^{2x} ?

The solution for (D^2-5D+6)y=3e^{3x}+e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}+3xe^{3x}-e^{2x}x

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

6 y^{^{'''}} + 4 y^{^{'}} = e^{x} cos (2 x)

4 y^{^{''}} + 25 y = 41 e^{2 x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 2 y = 3 e^{x}

y^{^{''}} - 8 y^{^{'}} + 2 y = t e^{t}

What is the solution for (D^2-5D+6)y=3e^{3x}+e^{2x} ?
The solution for (D^2-5D+6)y=3e^{3x}+e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}+3xe^{3x}-e^{2x}x