What is the solution for y^{''}-6y^'+9y=25e^tsin(t) ?

The solution for y^{''}-6y^'+9y=25e^tsin(t) is y=c_{1}e^{3t}+c_{2}te^{3t}+3e^tsin(t)+4e^tcos(t)

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y^{''}-6y^'+9y=25e^tsin(t)

y^{^{''}} - 6 y^{^{'}} + 9 y = 25 e^{t} sin (t)

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + 3 e^{t} sin (t) + 4 e^{t} cos (t)

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = 25 e^{t} sin (t)

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + 3 e^{t} sin (t) + 4 e^{t} cos (t)

y = c_{1} e^{3 t} + c_{2} t e^{3 t} + 3 e^{t} sin (t) + 4 e^{t} cos (t)

(D^{2} + 7 D + 6) y = e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = ln (x)

y^{^{''}} = 2 y + 18 tan^{3} (x)

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

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

What is the solution for y^{''}-6y^'+9y=25e^tsin(t) ?
The solution for y^{''}-6y^'+9y=25e^tsin(t) is y=c_{1}e^{3t}+c_{2}te^{3t}+3e^tsin(t)+4e^tcos(t)