What is the solution for 4q^{''}+8q^'+1/(0.0125)q=88q ?

The solution for 4q^{''}+8q^'+1/(0.0125)q=88q is q(t)=c_{1}e^{(-1+sqrt(3))t}+c_{2}e^{(-1-sqrt(3))t}

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4q^{''}+8q^'+1/(0.0125)q=88q

4 q^{^{''}} + 8 q^{^{'}} + \frac{1}{0.0125} q = 88 q

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

Solution steps

4 q^{''} (t) + 8 q^{'} (t) + \frac{1}{0.0125} q (t) = 88 q (t)

Solve linear ODE:

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

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

x^{^{''}} + 64 x = 0, x (0) = 0

y^{^{''}} - 256 y = 0

(D^{3} - 6 D^{2} + 5 D) y = 0

y^{^{''''}} - 6 y^{^{''}} + 9 y = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0

What is the solution for 4q^{''}+8q^'+1/(0.0125)q=88q ?
The solution for 4q^{''}+8q^'+1/(0.0125)q=88q is q(t)=c_{1}e^{(-1+sqrt(3))t}+c_{2}e^{(-1-sqrt(3))t}