Question

Find the general solution to the differential equation using variation of parameters:

Answer 1

Using variation of parameter method we solve the given differential equation.
Given the differential equation ने 7 ya = The Letry= A my be the triccial solution of the complementary function. Auxiliary equation m²=0 = m = 0,0 .. Complementary funetion (fel) = (4 +6,4) e 0.1 ☆ Ye (x) = 4+G* are arbitrany constant. where ů and 2

Let, yi(n) = 1 ya (1) = x, g(x)= e Then woly 1, Y2)= 10 7624 solution. bo, yo(a) and yel yz (a) are two line anly independent Let, ybaya 01(a) yola) + 69 (0) Yala) be the fun tiewan Soluton . 6. (3 freko 200 where, a 12 ) du a - - fx3da =-4 a4 [Jxndx = wrth Y -a4 76 v (a) = y (x)g (M) dx w(Y 1,42) -J'entendre = $ frede - [8] 02+1 [' fundes x nti 23 12 yp (a) = (x) y, (a) + 4,1) 7(x) (0) + () 4 x 76 + 24 To 12 3x4 +404 48 x4 48

:: General Solution of the giver differential equation is y = ye (") + Yolas ly = 6 +Cat 24 48