Question

If 8(x)=7cos 9x, in T13) then suggested form of y(x) is: [A] 7sin Ar+7cos Br [B] Asim 9x. [C] Asin 9x+Bcos 9x. ID] Bcos 9x [E]none. 2jf g(x) = 7e", in 773) and y e " + exe". G. ER in T1). then final form of y,(x) is: (AJA [B]Are [C]Are [D]Ac" + Hre" [E]none. 3)The general solution of y"+ 4y = 12, is: [4][ya = sin 2x+c, cos2x+12,6%, ER] [B][yo = sin 2x+c.cos2x+3,4,,ER] C%=+ce +3,9,6, ER] [D).=+ce* +34,6,,C,ER] Enone,

Answer 1

1. If g(x) = 7 cas 9x Then yp (X) = ? And Ip(x) = Asin 9x + B Cos 9x as cosax has decinative as a singa o we have to consider sin 9x un Jp (x) 2. If g(x) = 7 ex and Ye (x) = 469x + 2 xe 9+, G, GEIR Ang Up (x) = A 2 9x as 89%, xe ax is present in complementary solution 8 x ²x e 9 will be present in Yp(x). ag CR.H.SI 3. General solution of y"+4y= 12 is Seth y (x) = Yc (x) + Uplx Particular soln. General son complementary Soln For Yelx), Auxiliary ear is m² + 4 =0 m=t9 i

ye(x) = Goes & Yc (%) = 4 sin 2x + 6 cos2x. Que fore Yp(x) Let Yp(x) = A as R. HS 12 ( constant) Yp (x) = 0 Y" (X) =0 i. Yp + "Yp= 12 (as Up satisfy diff equ ) a 0+4A=12 U A =12 (A=3) . Yp(x)=3 8. y(x) = q sina x + C Cosax +3, G, C, EIR