What is the solution for y^{''}-3y^'+2y=9e^{3x} ?

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

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y^{''}-3y^'+2y=9e^{3x}

y^{^{''}} - 3 y^{^{'}} + 2 y = 9 e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{9}{2} e^{3 x}

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = 9 e^{3 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{9}{2} e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{9}{2} e^{3 x}

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

y^{^{''}} + 4 y = t^{2} + 6 e^{t}

y^{^{''}} - 2 y^{^{'}} + 5 y = 10 x^{2} - 3 x - 3

y^{^{''}} + 4 y = 3 cos (x)

y^{^{''}} - 8 y^{^{'}} + 4 y = x e^{x}

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