chapter2.page09

chapter2.page09 - ω t as integrant and t as integration...

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3. LINEAR EQUATIONS AND BERNOULLI EQUATIONS 9 Click on the Figure 4. Greek Letter Button which will bring up Figure 5. Greek Letter Bar and select the ω letter. Now if we rewrite and put in A ( t ) dT t = k ( A - T ) , we get dT t = k (80 - 10cos( ωt )) - kT, and is a linear equation with a ( t ) = k and b ( t ) = k (80 - 10cos( ωt )), it easy to see that R a ( t ) dt = R k dt = kt. Apply the solution formula we have T ( t ) = e - kt ˆ Z ke kt ± 80 - 10cos( ωt ) dt + C ! . After bring up the indeﬁnite operator Z d type k*e^k*t (80-10cos(
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Unformatted text preview: ω t) as integrant and t as integration vari-able, press [Ctrl][.], click any place outside the box, we get, Z ke kt ± 80-10 cos( ωt ) ¶ dt = 80 e kt-10 k ± k k 2 + ω 2 e kt cos( ωt )+ ω k 2 + ω 2 e-kt sin( ωt ) ¶ So the solution is T ( t ) = e-kt ˆ 80 e kt-10 k ± k k 2 + ω 2 e kt cos( ωt )+ ω k 2 + ω 2 e kt sin( ωt ) ¶ + C !...
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.

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