What is the solution for y^{''}-8y^'+15y=9xe^{2x} ?

The solution for y^{''}-8y^'+15y=9xe^{2x} is y=c_{1}e^{5x}+c_{2}e^{3x}+3xe^{2x}+4e^{2x}

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y^{''}-8y^'+15y=9xe^{2x}

y^{^{''}} - 8 y^{^{'}} + 15 y = 9 x e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{3 x} + 3 x e^{2 x} + 4 e^{2 x}

Solution steps

y^{''} (x) - 8 y^{'} (x) + 15 y = 9 x e^{2 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{3 x} + 3 x e^{2 x} + 4 e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{3 x} + 3 x e^{2 x} + 4 e^{2 x}

y^{^{''}} + 2 y^{^{'}} + y = 4 x

2 y^{^{''}} - 7 y^{^{'}} + 3 y = 5 e^{2 x}

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 3 + e^{- 2 x}

\frac{d ^{2} y}{d x ^{2}} - 9 y = e^{x} (1 + x)

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 6

What is the solution for y^{''}-8y^'+15y=9xe^{2x} ?
The solution for y^{''}-8y^'+15y=9xe^{2x} is y=c_{1}e^{5x}+c_{2}e^{3x}+3xe^{2x}+4e^{2x}