What is the solution for y^{''}+5y^'+6y=12e^t,y(0)=-11,y(0)=31 ?

The solution for y^{''}+5y^'+6y=12e^t,y(0)=-11,y(0)=31 is y=(-c_{2}-12)e^{-2t}+c_{2}e^{-3t}+e^t

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y^{''}+5y^'+6y=12e^t,y(0)=-11,y(0)=31

y^{^{''}} + 5 y^{^{'}} + 6 y = 12 e^{t}, y (0) = - 11, y (0) = 31

y = (- c_{2} - 12) e^{- 2 t} + c_{2} e^{- 3 t} + e^{t}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 12 e^{t}

Solve linear ODE:

y = (- c_{2} - 12) e^{- 2 t} + c_{2} e^{- 3 t} + e^{t}

y = (- c_{2} - 12) e^{- 2 t} + c_{2} e^{- 3 t} + e^{t}

y^{^{''}} + y^{^{'}} - y = t^{3}

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{x s e c (x)}

y^{^{''}} + y^{^{'}} = e^{2 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 3 t^{2} + 4 + e^{2 t} + t sin (2 t)

\frac{d ^{2} y}{d x ^{2}} + 9 y = 2 sec (3 x)

What is the solution for y^{''}+5y^'+6y=12e^t,y(0)=-11,y(0)=31 ?
The solution for y^{''}+5y^'+6y=12e^t,y(0)=-11,y(0)=31 is y=(-c_{2}-12)e^{-2t}+c_{2}e^{-3t}+e^t