What is the solution for y^{''}-6y^'+9y=10e^{3x} ?

The solution for y^{''}-6y^'+9y=10e^{3x} is y=c_{1}e^{3x}+c_{2}xe^{3x}+5x^2e^{3x}

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y^{''}-6y^'+9y=10e^{3x}

y^{^{''}} - 6 y^{^{'}} + 9 y = 10 e^{3 x}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 5 x^{2} e^{3 x}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 9 y = 10 e^{3 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 5 x^{2} e^{3 x}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 5 x^{2} e^{3 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{e ^{- 2 x}}{1 + x ^{2}}

y^{^{''''}} + 7 y^{^{''}} + 6 = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 11 e^{3 x}

y^{^{''}} + 3 y = 6 t^{3}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 10 y^{^{'}} + 41 y = 68 e^{4 t}

What is the solution for y^{''}-6y^'+9y=10e^{3x} ?
The solution for y^{''}-6y^'+9y=10e^{3x} is y=c_{1}e^{3x}+c_{2}xe^{3x}+5x^2e^{3x}