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Victor Ivrii

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Q5 TUT 0801
« on: November 02, 2018, 03:17:54 PM »
Transform the given initial value problem into an initial value problem for two first order equations.
$$\left\{\begin{aligned}
&u'' + 0.25u' + 4u = 2 \cos (3t),\\
&u(0) = 1,\qquad u'(0) = -2.
\end{aligned}\right.$$
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Guanyao Liang

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Re: Q5 TUT 0801
« Reply #1 on: November 02, 2018, 03:58:09 PM »
Answer in the attachment.
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Zhiya Lou

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Re: Q5 TUT 0801
« Reply #2 on: November 02, 2018, 04:13:29 PM »
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:$x_1(0)=1, x_2(0)= -2$
« Last Edit: November 02, 2018, 04:15:39 PM by Zhiya Lou »
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