Question

Differential equations / which pair of functions below cannot be a fundrmental set of solutions?

6. Which pair of functions below cannot be a fundamental set of solutions? (8 Points) 1, x3, xinx 3 cost + 6 sint, 5 cost + 10 sint €2x cos 3x + sin 3x, 1 e-31 3 te-31 5et + 5, 2e + 1

Answer 1

LeuЧ-Т, Ч,- м> Ч- n3 inn (9,, 9, 9) » 9 ч, у ch 93 ч, ч," 11 Ч, 1 () 13 hurgu اہ kuruetak № 9 2 439 + 6 ХҮҮ * ) = (Cuuүдяг.) 49 – (cuү«9 +ws) * * 81-9 - 31**51 3 + 16 счь - ... w ( 9, ч., , ) +о The functions 1, 13, 13 nu are fundamental solutions. set of

92= 5 cost tlosint Let y,= 3 cost tosint wcy,,4212 y2 y, y,' y 3 cost tosint 5 cost tlosint tsoaat tuuge- -5 sint & locost - (3 cost tosint) (-s sint t10 cost) :-( 5 cost tlo sint 16-3 Sintt6 cost) = - is sintcost to dost tis sint cost -30cost +3% sint -30 Sixtrost - 3osan't + 30 Sint cost wly,,4)=0 : The functions 3 cost tosint, scost +18 fint canot be a fundamental set of solutions.

9. 5 cos 1 + Sin37 , × 3 1 / 3 Let y, = een 9 1 9. ฯ 3 ง (99292- ich ih is 9," ฯ" ฯ" ( OS 31 + ติท37 -3in1+ScoS3ๆ 0 ใeS -ใcoS21-1ท? C D +0+ +[32"(-cos3ๆ - ให81) - ๆ ใฯ(-3โM3143e31) (99,93) - ฯ ( - Cos3พ - พฯ 45431-(8521) -Sue cost : 0 The functions e3", cos3n+sinsn, I are fundamental Set of solutions. Let Y,=est A ง: 6 0 uS(99)- 9, ฯ test 50 ง! - -36 -3te3te3t

wly,,Y) #0 fundamental set of solutions " e3t [-3te3t test] - test(-3636) - 3tl6ot test +36e3t Wly, 1421 2é ot to The functions e3t test are fundamental set of solutions. y,= =sen +5 2=2enti , wly1,42) y, Y2 50"+5 2+1 y,' yal sen zen = (sentslzen (zentiisen = 10ext loen 10ean-sen -sen The functions sents, 28"+1 are