Question

Consider the second order ODE:\\ $a\frac{d^2y}{dt^2} + b\frac{dy}{dt} + cy(t) = d$,\\subject to the initial conditions,\\ $y(0) = -5, \frac{dy}{dt}(0) = -8$,\\where $a = 4$, $b = 12$, $c = 3$, and $d = 9$. The solution to this ODE will be of the general form\\$y(t) = A_1e^{s_1t} + A_2e^{s_2t} + y_f$,\\where ($s_1, s_2$) are the two real roots of the characteristic equation, $y_f$ is a constant that represents\\the final value of the solution, and ($A_1, A_2$) are constants. Take $s_1$ to be the larger (less negative)\\and $s_2$ to be the smaller (more negative) of the two roots. Find the value of $s_1$ in units of rad/sec.

          Consider the second order ODE:\\
$a\frac{d^2y}{dt^2} + b\frac{dy}{dt} + cy(t) = d$,\\subject to the initial conditions,\\
$y(0) = -5, \frac{dy}{dt}(0) = -8$,\\where $a = 4$, $b = 12$, $c = 3$, and $d = 9$. The solution to this ODE will be of the general form\\$y(t) = A_1e^{s_1t} + A_2e^{s_2t} + y_f$,\\where ($s_1, s_2$) are the two real roots of the characteristic equation, $y_f$ is a constant that represents\\the final value of the solution, and ($A_1, A_2$) are constants. Take $s_1$ to be the larger (less negative)\\and $s_2$ to be the smaller (more negative) of the two roots. Find the value of $s_1$ in units of rad/sec.

Consider the second order ODE:

a(d^2y)/(dt^2) + b(dy)/(dt) + cy(t) = d,
subject to the initial conditions,

y(0) = -5, (dy)/(dt)(0) = -8,
where a = 4, b = 12, c = 3, and d = 9. The solution to this ODE will be of the general form
y(t) = A1e^s1t + A2e^s2t + yf,
where (s1, s2) are the two real roots of the characteristic equation, yf is a constant that represents
the final value of the solution, and (A1, A2) are constants. Take s1 to be the larger (less negative)
and s2 to be the smaller (more negative) of the two roots. Find the value of s1 in units of rad/sec.

Added by Emilio B.

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