Question

Consider the second order differential equation with initial conditions $u'' + 6.5u' + 6u = -6 \sin(3t)$, $u(1) = -4.5$, $u'(1) = -3$. Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter u to represent the function u and the single letter v to represent the \"velocity function\" $u'$. Do not use $u(t)$ or $v(t)$ to represent these functions. Expressions like $\sin(t)$ that represent other functions are OK. $u' = $ $v' = $ Now write the first order system using matrices: $\frac{d}{dt} \begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} \\ \\ \end{bmatrix} \begin{bmatrix} u \\ v \end{bmatrix} + \begin{bmatrix} \\ \end{bmatrix}$. The initial value of the vector valued solution for this system is: $\begin{bmatrix} u(1) \\ v(1) \end{bmatrix} = \begin{bmatrix} \\ \end{bmatrix}$.

          Consider the second order differential equation with initial conditions
$u'' + 6.5u' + 6u = -6 \sin(3t)$, $u(1) = -4.5$, $u'(1) = -3$.
Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter u to represent the function u and the
single letter v to represent the \"velocity function\" $u'$. Do not use $u(t)$ or $v(t)$ to represent these functions. Expressions like $\sin(t)$ that represent other functions are OK.
$u' = $
$v' = $
Now write the first order system using matrices:
$\frac{d}{dt} \begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} \\ \\ \end{bmatrix} \begin{bmatrix} u \\ v \end{bmatrix} + \begin{bmatrix} \\ \end{bmatrix}$.
The initial value of the vector valued solution for this system is:
$\begin{bmatrix} u(1) \\ v(1) \end{bmatrix} = \begin{bmatrix} \\ \end{bmatrix}$.

Consider the second order differential equation with initial conditions
u” + 6.5u' + 6u = -6 sin(3t), u(1) = -4.5, u'(1) = -3.
Without solving it, rewrite the differential equation as an equivalent set of first order equations. In your answer use the single letter u to represent the function u and the
single letter v to represent the v̈elocity function$̈u'. Do not useu(t)orv(t)to represent these functions. Expressions likesin(t)that represent other functions are OK.u' = v' = Now write the first order system using matrices:(d)/(dt)
< b m a t r i x >
=
< b m a t r i x >

< b m a t r i x >
+
< b m a t r i x >
.
The initial value of the vector valued solution for this system is:
< b m a t r i x >
=
< b m a t r i x >
.

Added by Matthew B.

Question

Please give Ace some feedback