What is the solution for y^{''}+9y^'+17y=0 ?

The solution for y^{''}+9y^'+17y=0 is y=c_{1}e^{((-9+sqrt(13))t)/2}+c_{2}e^{((-9-sqrt(13))t)/2}

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y^{''}+9y^'+17y=0

y^{^{''}} + 9 y^{^{'}} + 17 y = 0

y = c_{1} e^{\frac{( - 9 + 13 ) t}{2}} + c_{2} e^{\frac{( - 9 - 13 ) t}{2}}

Solution steps

y^{''} (t) + 9 y^{'} (t) + 17 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 9 + 13 ) t}{2}} + c_{2} e^{\frac{( - 9 - 13 ) t}{2}}

y = c_{1} e^{\frac{( - 9 + 13 ) t}{2}} + c_{2} e^{\frac{( - 9 - 13 ) t}{2}}

y^{^{''}} - y = 0, y (1) = 1, y (2) = 0

y^{^{''}} + 4 y^{^{'}} + y 5 = 0

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = - 3, y^{^{'}} (0) = - 4

y^{^{''}} + 3 y = 0, y^{0} = 1, y^{^{'}} 0 = 3

What is the solution for y^{''}+9y^'+17y=0 ?
The solution for y^{''}+9y^'+17y=0 is y=c_{1}e^{((-9+sqrt(13))t)/2}+c_{2}e^{((-9-sqrt(13))t)/2}