What is the solution for y^{''}+10y^'+8y=0 ?

The solution for y^{''}+10y^'+8y=0 is y=c_{1}e^{(-5+sqrt(17))t}+c_{2}e^{(-5-sqrt(17))t}

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y^{''}+10y^'+8y=0

y^{^{''}} + 10 y^{^{'}} + 8 y = 0

y = c_{1} e^{(- 5 + 17) t} + c_{2} e^{(- 5 - 17) t}

Solution steps

y^{''} (t) + 10 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = c_{1} e^{(- 5 + 17) t} + c_{2} e^{(- 5 - 17) t}

y = c_{1} e^{(- 5 + 17) t} + c_{2} e^{(- 5 - 17) t}

y^{^{'''}} + 8 y^{^{''}} + 19 y^{^{'}} + 12 y = 0

y^{^{''}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = 4

81 y^{^{''}} + 108 y^{^{'}} - 13 y = 0, y (0) = 1, y^{^{'}} (0) = 0

x^{^{''}} + 0.5 x^{^{'}} + 4 x = 0

x^{^{''}} - c^{2} x = 0

What is the solution for y^{''}+10y^'+8y=0 ?
The solution for y^{''}+10y^'+8y=0 is y=c_{1}e^{(-5+sqrt(17))t}+c_{2}e^{(-5-sqrt(17))t}