What is the solution for y^{''}+9y^'+12y=0 ?

The solution for y^{''}+9y^'+12y=0 is y=c_{1}e^{((-9+sqrt(33))t)/2}+c_{2}e^{((-9-sqrt(33))t)/2}

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y^{''}+9y^'+12y=0

y^{^{''}} + 9 y^{^{'}} + 12 y = 0

y = c_{1} e^{\frac{( - 9 + 33 ) t}{2}} + c_{2} e^{\frac{( - 9 - 33 ) t}{2}}

Solution steps

y^{''} (t) + 9 y^{'} (t) + 12 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 9 + 33 ) t}{2}} + c_{2} e^{\frac{( - 9 - 33 ) t}{2}}

y = c_{1} e^{\frac{( - 9 + 33 ) t}{2}} + c_{2} e^{\frac{( - 9 - 33 ) t}{2}}

3 y^{^{''}} - 16 y^{^{'}} + 13 y = 0

y^{^{''}} + n^{2} y = 0, y (0) = c, y^{^{'}} (0) = v

4 y^{^{''}} - 8 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = \frac{1}{2}

24 y^{^{''}} + 2.2 y = 0

y^{^{''}} + 30 y^{^{'}} + a y = 0

What is the solution for y^{''}+9y^'+12y=0 ?
The solution for y^{''}+9y^'+12y=0 is y=c_{1}e^{((-9+sqrt(33))t)/2}+c_{2}e^{((-9-sqrt(33))t)/2}