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

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

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

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

y = 4 e^{- 3 t} - 3 e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = 4 e^{- 3 t} - 3 e^{- 4 t}

y = 4 e^{- 3 t} - 3 e^{- 4 t}

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\frac{d}{d x} (- \frac{72}{( x + 2 ) ^{4}})

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