Toronto Math Forum
MAT2442018F => MAT244Tests => Quiz5 => Topic started by: Victor Ivrii on November 02, 2018, 03:17:54 PM

Transform the given initial value problem into an initial value problem for two first order equations.
$$\left\{\begin{aligned}
&u'' + 0.25u' + 4u = 2 \cos (3t),\\
&u(0) = 1,\qquad u'(0) = 2.
\end{aligned}\right.$$

Answer in the attachment.

Let $x_1= u, x_2=u'$
Then substitute it into original equation:
$ x_2'+0.25x_2+4x_1 = 2\cos(3t)$
So, we can transform into the system:
$x_1'=x_2$
$ x_2'+0.25x_2+4x_1 = 2\cos(3t)$
With given initial value:$x_1(0)=1, x_2(0)= 2$