What is the solution for y^{''}-6y^'+9y=4e^x ?

The solution for y^{''}-6y^'+9y=4e^x is y=c_{1}e^{3x}+c_{2}xe^{3x}+e^x

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y^{''}-6y^'+9y=4e^x

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 e^{x}

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

Solution steps

y^{''} (x) - 6 y^{'} (x) + 9 y = 4 e^{x}

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 7 y = t e^{t}

y^{^{''}} + 9 y = sin (2 x), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y = 8 sin (2 x) + 5 e^{x}

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12 x, y (0) = 1, y^{^{'}} (0) = - 2

y^{^{''}} + 25 y = 82 e^{4 x}

What is the solution for y^{''}-6y^'+9y=4e^x ?
The solution for y^{''}-6y^'+9y=4e^x is y=c_{1}e^{3x}+c_{2}xe^{3x}+e^x