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

The solution for y^{''}+5y^'+6y=0 is y=c_{1}e^{-2t}+c_{2}e^{-3t}

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y^{''}+5y^'+6y=0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t}

y^{^{''}} + 3 y = 9

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3 x})

\int 4 r^{2} + 1 r d r

\frac{d}{d x} (arccos (\frac{x}{8}))

\frac{d}{d x} (π^{x})

What is the solution for y^{''}+5y^'+6y=0 ?
The solution for y^{''}+5y^'+6y=0 is y=c_{1}e^{-2t}+c_{2}e^{-3t}