- #1

karush

Gold Member

MHB

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transform the given equation into a system of first order equation$$u''+0.5u'+2u=0$$ok from examples it looks all we do is get rid of some of the primes and this is done by substitutionso 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 ?

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 ?

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