What is the solution for y^{''}+7y^'+12y=0,y(0)=1,y^'(0)=-9 ?

The solution for y^{''}+7y^'+12y=0,y(0)=1,y^'(0)=-9 is y=-5e^{-3t}+6e^{-4t}

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y^{''}+7y^'+12y=0,y(0)=1,y^'(0)=-9

y^{^{''}} + 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 9

y = - 5 e^{- 3 t} + 6 e^{- 4 t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 12 y = 0

Solve linear ODE:

y = - 5 e^{- 3 t} + 6 e^{- 4 t}

y = - 5 e^{- 3 t} + 6 e^{- 4 t}

y^{^{''}} - 9 y^{^{'}} - 3 y = 0

y^{^{''''}} - 10 y^{^{''}} + 25 y = 0

\frac{y ^{^{''}}}{8} + 5 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = - 5

- 1 y^{^{''}} + 10 y = 0, y (0) = 1, y (1) = 0

25 x^{^{''}} + 90 x^{^{'}} + 81 x = 0

What is the solution for y^{''}+7y^'+12y=0,y(0)=1,y^'(0)=-9 ?
The solution for y^{''}+7y^'+12y=0,y(0)=1,y^'(0)=-9 is y=-5e^{-3t}+6e^{-4t}