What is the solution for y^{''}-6y^'-2y=0 ?

The solution for y^{''}-6y^'-2y=0 is y=c_{1}e^{(3+sqrt(11))t}+c_{2}e^{(3-sqrt(11))t}

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

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

y = c_{1} e^{(3 + 11) t} + c_{2} e^{(3 - 11) t}

Solution steps

y^{''} (t) - 6 y^{'} (t) - 2 y = 0

Solve linear ODE:

y = c_{1} e^{(3 + 11) t} + c_{2} e^{(3 - 11) t}

y = c_{1} e^{(3 + 11) t} + c_{2} e^{(3 - 11) t}

y^{^{'''}} + y^{^{''}} + 2 y^{^{'}} + 2 y = 0

y^{^{''}} + 4 y = 0, y (\frac{π}{4}) = 3, y (0) = 5

y^{^{'''}} - 4 y^{^{''}} - 16 y^{^{'}} + 64 y = 0

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

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

What is the solution for y^{''}-6y^'-2y=0 ?
The solution for y^{''}-6y^'-2y=0 is y=c_{1}e^{(3+sqrt(11))t}+c_{2}e^{(3-sqrt(11))t}