What is the solution for y^{''}+5y^'+y=0 ?

The solution for y^{''}+5y^'+y=0 is y=c_{1}e^{((-5+sqrt(21))t)/2}+c_{2}e^{((-5-sqrt(21))t)/2}

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y^{''}+5y^'+y=0

y^{^{''}} + 5 y^{^{'}} + y = 0

y = c_{1} e^{\frac{( - 5 + 21 ) t}{2}} + c_{2} e^{\frac{( - 5 - 21 ) t}{2}}

Solution steps

y^{''} (t) + 5 y^{'} (t) + y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 5 + 21 ) t}{2}} + c_{2} e^{\frac{( - 5 - 21 ) t}{2}}

y = c_{1} e^{\frac{( - 5 + 21 ) t}{2}} + c_{2} e^{\frac{( - 5 - 21 ) t}{2}}

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What is the solution for y^{''}+5y^'+y=0 ?
The solution for y^{''}+5y^'+y=0 is y=c_{1}e^{((-5+sqrt(21))t)/2}+c_{2}e^{((-5-sqrt(21))t)/2}