MAT244--2018F > Quiz-5

Q5 TUT 0801

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Victor Ivrii:
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.

Guanyao Liang:

Zhiya Lou:
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:$x_1(0)=1, x_2(0)= -2$