What is the solution for y^{''}+5y^'+6y=36e^t,y(0)=-5,y^'(0)=21 ?

The solution for y^{''}+5y^'+6y=36e^t,y(0)=-5,y^'(0)=21 is y=-6e^{-2t}-2e^{-3t}+3e^t

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y^{''}+5y^'+6y=36e^t,y(0)=-5,y^'(0)=21

y^{^{''}} + 5 y^{^{'}} + 6 y = 36 e^{t}, y (0) = - 5, y^{^{'}} (0) = 21

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

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 36 e^{t}

Solve linear ODE:

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

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

What is the solution for y^{''}+5y^'+6y=36e^t,y(0)=-5,y^'(0)=21 ?
The solution for y^{''}+5y^'+6y=36e^t,y(0)=-5,y^'(0)=21 is y=-6e^{-2t}-2e^{-3t}+3e^t