What is the solution for y^{''}+15y^'+56y=0,y(0)=11,y^'(0)=-85 ?

The solution for y^{''}+15y^'+56y=0,y(0)=11,y^'(0)=-85 is y=3e^{-7t}+8e^{-8t}

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y^{''}+15y^'+56y=0,y(0)=11,y^'(0)=-85

y^{^{''}} + 15 y^{^{'}} + 56 y = 0, y (0) = 11, y^{^{'}} (0) = - 85

y = 3 e^{- 7 t} + 8 e^{- 8 t}

Solution steps

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

Solve linear ODE:

y = 3 e^{- 7 t} + 8 e^{- 8 t}

y = 3 e^{- 7 t} + 8 e^{- 8 t}

4 y^{^{''}} = - 25 y

2500 y^{^{''}} + 729 y = 0, y (0) = 2, y^{^{'}} (0) = 3

x^{^{''}} + 8 x^{^{'}} + 10 x = 0, x (0) = 10, x^{^{'}} (0) = 0

2500 y^{^{''}} + 729 y = 0, y (0) = 2, y^{^{'}} (0) = 5

35 y^{^{''''}} + 52 y^{^{''}} + 9 y = 0

What is the solution for y^{''}+15y^'+56y=0,y(0)=11,y^'(0)=-85 ?
The solution for y^{''}+15y^'+56y=0,y(0)=11,y^'(0)=-85 is y=3e^{-7t}+8e^{-8t}