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

The solution for y^{''}+9y^'-9y=0 is y=c_{1}e^{((-9+3sqrt(13))t)/2}+c_{2}e^{((-9-3sqrt(13))t)/2}

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

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

y = c_{1} e^{\frac{( - 9 + 3 13 ) t}{2}} + c_{2} e^{\frac{( - 9 - 3 13 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( - 9 + 3 13 ) t}{2}} + c_{2} e^{\frac{( - 9 - 3 13 ) t}{2}}

y = c_{1} e^{\frac{( - 9 + 3 13 ) t}{2}} + c_{2} e^{\frac{( - 9 - 3 13 ) t}{2}}

8 y - 2 y^{^{'}} + 6 y^{^{''}} - y^{^{''}} = 0

y^{^{''}} + 6 y - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} - 11 y + 18 y = 0

y^{^{''}} + v y^{^{'}} = 0

2 x^{^{''}} + 11 x^{^{'}} + 5 x = 0

What is the solution for y^{''}+9y^'-9y=0 ?
The solution for y^{''}+9y^'-9y=0 is y=c_{1}e^{((-9+3sqrt(13))t)/2}+c_{2}e^{((-9-3sqrt(13))t)/2}