What is the solution for y^{''}-6y^'+9y=e^{2t} ?

The solution for y^{''}-6y^'+9y=e^{2t} is y=c_{1}e^{3t}+c_{2}te^{3t}+e^{2t}

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y^{''}-6y^'+9y=e^{2t}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{2 t}

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

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = e^{2 t}

Solve linear ODE:

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

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

(D^{4} - 1) \cdot y = sin (2 x)

y^{^{''}} + y^{^{'}} - 7 y = 42 t

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

y^{^{''}} - 6 y^{^{'}} - 9 y = x^{2} + e^{x}

x^{^{''}} + 5 x^{^{'}} + 4 x = t^{2} + 3 t + 5

What is the solution for y^{''}-6y^'+9y=e^{2t} ?
The solution for y^{''}-6y^'+9y=e^{2t} is y=c_{1}e^{3t}+c_{2}te^{3t}+e^{2t}