What is the solution for y^{''}+4y^'+(a^2-2)y=0 ?

The solution for y^{''}+4y^'+(a^2-2)y=0 is y=c_{1}e^{(-2+sqrt(-a^2+6))t}+c_{2}e^{(-sqrt(-a^2+6)-2)t}

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y^{''}+4y^'+(a^2-2)y=0

y^{^{''}} + 4 y^{^{'}} + (a^{2} - 2) y = 0

y = c_{1} e^{(- 2 + - a^{2} + 6) t} + c_{2} e^{(- - a^{2} + 6 - 2) t}

Solution steps

y^{''} (t) + 4 y^{'} (t) + (a^{2} - 2) y = 0

Solve linear ODE:

y = c_{1} e^{(- 2 + - a^{2} + 6) t} + c_{2} e^{(- - a^{2} + 6 - 2) t}

y = c_{1} e^{(- 2 + - a^{2} + 6) t} + c_{2} e^{(- - a^{2} + 6 - 2) t}

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

25 x^{^{''}} + 5 x^{^{'}} + 204.167 x = 0, x (0) = 28.577

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 4

\frac{d ^{2} y}{d t ^{2}} - 14 \frac{d y}{d t} + 149 y = 0

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

What is the solution for y^{''}+4y^'+(a^2-2)y=0 ?
The solution for y^{''}+4y^'+(a^2-2)y=0 is y=c_{1}e^{(-2+sqrt(-a^2+6))t}+c_{2}e^{(-sqrt(-a^2+6)-2)t}