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# quiz3b - NIath 415 Quiz 3 Name TA Younghwan Son Rec Time...

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Unformatted text preview: NIath 415 Quiz 3 Name: _________________________ TA: Younghwan Son Rec. Time: _____________________ Form B Show all work; answers with insufﬁcient support will not receive credit. GOOD LUCK! 1.Find the solutions y1, y2 for the diﬁerential equation y” + 431’ + 3y = 0, where yl satisﬁes y1(1) = 1,y’1(1) = 0 and y2 satisﬁes y2(1) = 0,y’2(1) = 1 macfeym‘z‘z 99m : rl+4r +3=o v9 (V+\)(r+3)=o ~ i=4, —3 (Tammi S’al : 7: Cl e-ci—I) + C; e—Mé-b) F0, )3, Z(l;=o => CI+CJ=° )L’fu: | =7 "C: -353 =- - é- - (é—I) y) _ ief I) -1.- C 3 2. If yl and 312 are solutions of y”+py’+qy = 0 and if ya = y1 +y2 and y4 = y1 —y2 are linearly independent, then show that yl and y2 are linearly independent. H'OM )f?:>Il+7-l, 74.2)[1’XL Heme X) )1 are Macaw IMP/endemf. ...
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