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=13e^{-3t}-12e^{-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 = 13 e^{- 3 t} - 12 e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = 13 e^{- 3 t} - 12 e^{- 4 t}

y = 13 e^{- 3 t} - 12 e^{- 4 t}

y^{^{''}} = - y^{^{'}} - y

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{4}) = 0, y^{^{'}} (\frac{π}{4}) = - 3

y^{^{''}} + (\frac{v}{a}) y^{^{'}} = 0

\frac{d ^{4} y}{d x ^{4}} - 2 (\frac{d ^{2} y}{d x ^{2}}) + y = 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=13e^{-3t}-12e^{-4t}