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#### karush

##### Well-known member

- Jan 31, 2012

- 2,886

$$u''+0.5u'+2u=0$$

ok from examples it looks all we do is get rid of some of the primes and this is done by substitution

so if $u_1=u$ and $u_2=u'_1$

then $u_2=u'$ and $u'_2=u''$

then we have $u'_2+0.5u_2 +2u_1 = 0$

then isolate $u'_2$ thus $u'_2=-0.5u_2-2u_1$

ok the next problem is

$$u''+0.5u'+2u=3\sin t$$ so ???