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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 8 y^{^{'}} + 16 y = - 5 e^{4 x} + \frac{e ^{4 x}}{x}

a y^{^{''}} + b y^{^{'}} + cy = g (t)

(d^{2} - 4) y = 2 x

y^{^{''}} + y^{^{'}} - 2 y = 2 t - 40 cos (2 t)

y^{^{''}} - 6 y^{^{'}} + 45 y = - 4 sin (2 t)

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