What is the solution for y^{''}-6y^'-12y=0 ?

The solution for y^{''}-6y^'-12y=0 is y=c_{1}e^{(3+sqrt(21))t}+c_{2}e^{(3-sqrt(21))t}

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y^{''}-6y^'-12y=0

y^{^{''}} - 6 y^{^{'}} - 12 y = 0

y = c_{1} e^{(3 + 21) t} + c_{2} e^{(3 - 21) t}

Solution steps

y^{''} (t) - 6 y^{'} (t) - 12 y = 0

Solve linear ODE:

y = c_{1} e^{(3 + 21) t} + c_{2} e^{(3 - 21) t}

y = c_{1} e^{(3 + 21) t} + c_{2} e^{(3 - 21) t}

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

y^{^{''}} - 8 y^{^{'}} - 105 y = 0

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 0

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

16 y^{^{''}} - 8 y^{^{'}} + y = 0, y (0) = - 4, y^{^{'}} (0) = 3

What is the solution for y^{''}-6y^'-12y=0 ?
The solution for y^{''}-6y^'-12y=0 is y=c_{1}e^{(3+sqrt(21))t}+c_{2}e^{(3-sqrt(21))t}