What is the solution for y^{''}+5y^'+6y=0,y(0)=2,y^'(0)=0 ?

The solution for y^{''}+5y^'+6y=0,y(0)=2,y^'(0)=0 is y=6e^{-2t}-4e^{-3t}

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y^{''}+5y^'+6y=0,y(0)=2,y^'(0)=0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y = 6 e^{- 2 t} - 4 e^{- 3 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 0

Solve linear ODE:

y = 6 e^{- 2 t} - 4 e^{- 3 t}

y = 6 e^{- 2 t} - 4 e^{- 3 t}

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\int z^{2} (\frac{1}{2 π} e^{- \frac{1}{2} z^{2}}) d z

\int 3 sin^{2} (x) d x

\frac{\partial}{\partial y} (x^{y} + ln (z))

What is the solution for y^{''}+5y^'+6y=0,y(0)=2,y^'(0)=0 ?
The solution for y^{''}+5y^'+6y=0,y(0)=2,y^'(0)=0 is y=6e^{-2t}-4e^{-3t}