What is the solution for y^{''}+5y^'-6y=21e^t ?

The solution for y^{''}+5y^'-6y=21e^t is y=c_{1}e^t+c_{2}e^{-6t}+3te^t

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y^{''}+5y^'-6y=21e^t

y^{^{''}} + 5 y^{^{'}} - 6 y = 21 e^{t}

y = c_{1} e^{t} + c_{2} e^{- 6 t} + 3 t e^{t}

Solution steps

y^{''} (t) + 5 y^{'} (t) - 6 y = 21 e^{t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- 6 t} + 3 t e^{t}

y = c_{1} e^{t} + c_{2} e^{- 6 t} + 3 t e^{t}

y^{^{''''}} + 2 y^{^{''}} + y = cos (2 x) + 2

y^{^{''}} - 2 y^{^{'}} + 5 y = 10 sin (x)

y^{^{''}} + \frac{1}{8} y^{^{'}} + y = 3 cos (x)

y^{^{''}} + 8 y^{^{'}} + 16 = 24 x + 2

y^{^{''}} - 8 y^{^{'}} = - 8 e^{- 2 x}

What is the solution for y^{''}+5y^'-6y=21e^t ?
The solution for y^{''}+5y^'-6y=21e^t is y=c_{1}e^t+c_{2}e^{-6t}+3te^t