What is the solution for y^{''}+15y^'+56y=0 ?

The solution for y^{''}+15y^'+56y=0 is y=c_{1}e^{-7t}+c_{2}e^{-8t}

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y^{''}+15y^'+56y=0

y^{^{''}} + 15 y^{^{'}} + 56 y = 0

y = c_{1} e^{- 7 t} + c_{2} e^{- 8 t}

Solution steps

y^{''} (t) + 15 y^{'} (t) + 56 y = 0

Solve linear ODE:

y = c_{1} e^{- 7 t} + c_{2} e^{- 8 t}

y = c_{1} e^{- 7 t} + c_{2} e^{- 8 t}

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t^{2} y^{^{'}} + y^{2} = t y

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What is the solution for y^{''}+15y^'+56y=0 ?
The solution for y^{''}+15y^'+56y=0 is y=c_{1}e^{-7t}+c_{2}e^{-8t}