What is the solution for y^{''}+6y^'+5y=12e^t,y(0)=-1,y^'(0)=7 ?

The solution for y^{''}+6y^'+5y=12e^t,y(0)=-1,y^'(0)=7 is y=-e^{-t}-e^{-5t}+e^t

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y^{''}+6y^'+5y=12e^t,y(0)=-1,y^'(0)=7

y^{^{''}} + 6 y^{^{'}} + 5 y = 12 e^{t}, y (0) = - 1, y^{^{'}} (0) = 7

y = - e^{- t} - e^{- 5 t} + e^{t}

Solution steps

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

Solve linear ODE:

y = - e^{- t} - e^{- 5 t} + e^{t}

y = - e^{- t} - e^{- 5 t} + e^{t}

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

D, D (t) = \frac{100 ln ( t + 2 )}{t + 2}

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 6 x^{2} + 5 x - 8

y^{^{''}} + 4 y = 2 cos (2 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{x} - 3

What is the solution for y^{''}+6y^'+5y=12e^t,y(0)=-1,y^'(0)=7 ?
The solution for y^{''}+6y^'+5y=12e^t,y(0)=-1,y^'(0)=7 is y=-e^{-t}-e^{-5t}+e^t