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

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

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y^{''}+6y^'+6y=0

y^{^{''}} + 6 y^{^{'}} + 6 y = 0

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

Solution steps

y^{''} (t) + 6 y^{'} (t) + 6 y = 0

Solve linear ODE:

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

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

y^{^{'}} = 2 t, y (0) = 1

\int \frac{2 x}{( x ^{2} + x + 1 )} d x

y^{^{'}} = \frac{3 x ^{7} e ^{\frac{y}{x}} + x ^{5} y ^{2}}{x ^{6} y}

x \to 2 lim (\frac{x - 7}{x + 3})

\int_{1}^{\infty} \frac{1}{x ^{3} - 1} d x

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