What is the solution for y^{''}+7y^'+12y=0,y(0)=2,y^'(0)=1 ?

The solution for y^{''}+7y^'+12y=0,y(0)=2,y^'(0)=1 is y=9e^{-3t}-7e^{-4t}

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y^{''}+7y^'+12y=0,y(0)=2,y^'(0)=1

y^{^{''}} + 7 y^{^{'}} + 12 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y = 9 e^{- 3 t} - 7 e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = 9 e^{- 3 t} - 7 e^{- 4 t}

y = 9 e^{- 3 t} - 7 e^{- 4 t}

\frac{d ^{2} x}{d t ^{2}} + c \cdot \frac{d x}{d t} + k \cdot x = 0

y^{^{''}} + 4 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

121 y^{^{''}} + 132 y^{^{'}} + 117 y = 0

x^{^{''}} + 4 x^{^{'}} + 3 x = 0, x (0) = 3

x^{^{''}} + 4 x^{^{'}} + 3 x = 0, x (0) = 2

What is the solution for y^{''}+7y^'+12y=0,y(0)=2,y^'(0)=1 ?
The solution for y^{''}+7y^'+12y=0,y(0)=2,y^'(0)=1 is y=9e^{-3t}-7e^{-4t}