What is the solution for y^{''}+2y^'+ay=0 ?

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

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

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

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

Solution steps

y^{''} (t) + 2 y^{'} (t) + a y = 0

Solve linear ODE:

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

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

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