What is the solution for y^{''}+4y^'+y=0 ?

The solution for y^{''}+4y^'+y=0 is y=c_{1}e^{(-2+sqrt(3))t}+c_{2}e^{(-2-sqrt(3))t}

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y^{''}+4y^'+y=0

y^{^{''}} + 4 y^{^{'}} + y = 0

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

Solution steps

y^{''} (t) + 4 y^{'} (t) + y = 0

Solve linear ODE:

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

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

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What is the solution for y^{''}+4y^'+y=0 ?
The solution for y^{''}+4y^'+y=0 is y=c_{1}e^{(-2+sqrt(3))t}+c_{2}e^{(-2-sqrt(3))t}