Question

1. Solve differential equation by variation of parameters 4y" – 4y' + y = ež V1 – 12 2. Solve differential equation by variation of parameters 2x y" – 34" + 2y = 1+ er

Answer 1

(am-) (2m-1) 20 O given 49" 4' +५= e Hor 1-x Homogeneous equation 49" 4y' +y 50 Characteristic ecuatlun 4m२- 4m +120 (2m-RO । m= २७ २७ Homogeneous Solution In = ue taxe ३ let Kor 4ce xe पू Hea Mod ५' जा (3+1) 91 ५२ W (9,42) प علم

1/2 wly, ) = xe sla x/2 ģt e x/2 e (+1) e et clor k you C 들이 - ex Ale +1 x a ex w 19,9] using variation of poremeter method let Up = 44, + Mg Y where reu) Yg u = -S2 doc لدا xlo Sinx X/ See e مهره en C = - fx since dx 2x) Ji-xa de let 312 g = Ź (1-x) 312 3/2 Ś (la se

U fi res de 04/12 et la Firx? da eu S Six da Since) + X V12 ง yp = (1-P)978 419 1/2 x simbe + 1/2 t e 2 e 3 general solutim is YUE) = yn typ 312 x sinbetreux? Mla t 903) = cekurg e*: (0 -Pop 9(x) = (4 +Gx) e ई 9(x) = (x +Gx)e * Exsinly Jinx? x + + 2 le rsione suze x*ca]e 12 3 + 3x since) + (x + 2) (x2) 2/2