Question

Please show all work with clear handwriting

a)

Compute the Wrornskian of the set {e* cos 3x, ex sin 3x}

Answer 1

we have to compute wronkian of set fee seda, et sinan} we know wronkicon of set Pfi(n), fz 193} Te given by : WB = ficar) fa (01) fz'() fi'ca) ;; wronkian of set ſ et corsa, elesin Ba} is given . by el cos ar ex sinzze - W= az (ERCO384) det (elsing) Cosa el sinza (1 ecos3x 7 afsins el cossa ex sinsze let cos3x-Belsina ex sin3x + 3 e² cosso 1) (ex cos3a)lesinga 13e corsa) — (pasin 33) (CACO CERTA Bersin34 s ere cose singe T3022 + 3er singa coszne 28 sin32 (osax

2 2x 22% (Sirts& pcos3x) e 28 (1) .: W= eze les cer wronkian of set frei corsa e?' sin sx} se $0 IW= 13 22 e Now Соде have to show lexcosse, ed single on form foundamental solution set for y? L2y4l0y=o interval felle cos3M, ed sin gay is solution set .. Firstly we show of Log' t coastet Jet you to y"_zy' proy so o Associated Auszeill goy equation is m²_. 2m +10=0 We find Root of ayseil day equation .: we know Roots of quachractic equation on am² tbm+c=0 is given by formula m = -b I J 6²-49c 29 roots of cepcillary equation is -(-) I J (21 ² 4x1x10 ma 21) 2 I r 4-40 . 21 1136 - 3451 2