Question

dj yp=é 2 Otwo linearly independene solotions of the I differential equation ý "+12ylt 36y=o are 064 Y₂ = Xe6x b) y,=0 Y = xe Y = 6x d Yizes Y = 0 6x Y = xe 6x Vi=e6x Y2= e 6x

12. specify which letter answer is correct

Answer 1

(12) The given differential equation is y" +124' +364 =0 1 solution of 6 is taken (A +0) then the auxiliary becomes m² 12m +3620 trial It the y = tema 2 equation (+6)=0 m = -6, -6 Soly tion Les general Of is (Cu+c8)es = Cie +Sxé 62 where constants. arbitrary ہو رہے are -62 Let 42 (21) = xe e ya are Then if and Y. wronskioon Lire anly independent Ye and 4 y of non - 22.10. Woons kian Ye and Yay Non Y. W(Y, Y2) = ya' é 6x xe 17 - се e é 6x6xe 6x *-622 12x -exe -12% + sxe 12x e +0 , XER.

equation always satisfy the differential ane 2 y (1) =é Y2 (2) = ne two linearly independent solutions given differential equation. that the solution of a differential we knon equation. For option (: - Y = e ex »y, aber ye" = 36e6x Y," +12 %, '4364, 6 x 720x 436e 6x 36e 0, teox (144) 70 txt R - e 62 : Y = e 6x y = efx is not the does not satisfy solution of given differential equation. not true. option For option bir 4x Here y, a = e y, (a) =qe 12 » Y."( W16893 y."(9) +124, (a +3644 4 NOO + 360 4X Ibe + 480 4X (70) , since e ax 40, & FR 10o e An

does : Yure 43 satisfy solution of the given is not true. not y = e Ad is not a differential equation, so option (6) For option ©):- By using Yare is not solution of given differential so option (e) is not true. equation. For option ) : Here y=et > y=0 y" 11 Ya = e not true. +124, +3646 0+0+ 366-6 ( 70) not satisfy yaa é 60 is not solution of the given differentiane equation, so option (as is For option (@: by using solution of the given equation. So option (e) is not true. NO option is consect Yaseen is not differential a