Question

2 e у". 6у " t 12y - -y" +3y" е е

is there anyone who can solve this problem?

Answer 1

O chare lan a 3 = 0 = m = 9 + y" - byl + 12 yl - 8y = x 0.5 x ₃0 for Homogeneous part y" - byl + 12yl - 8y=0 m² smd t2m-8=0 (m-2) Cm2 4m + 4) =0 (M-2) = 29899 Yp(x) = A 2X + Be Xa+ C2 2x fore payehicular zolution Consider YpCx) = 024.62048 28 Yploo - 2.5 02452@x+ 20%2524+3.58x35 ax +62) 85ce) eax + 4.5°F 23.5 8x + 272 4.5 ax Yp'(x) = (2.5) (1.5).D 20.5 + SDX5 2x + 50%! 2105 2x + UD25 't Dax 2 (3.5) € 47.52X +3.5) (9.5) Exl«5eQx + 4EX3-500x + 70X0 12.5, ax +9Px32x7(1-5)3.5) 22. 5 2x + Upg 4.5 3x + gf 23.5 x uring values of YP, Ye X" and Yill in 0 g we get ģ P=0 Yp(x) = yex) = A *x+ BX X + (x Pe X + 8 x 8 5 2x Andwa P & 4.5 ax D=0 9 80 105

@ xyl + 3y" = 2 > g" +3cu - xe for Homogeneous part x8yll + 3x²y"=0 & Cauchy Euler} diff. En DCD-1) (0-2) + 3 D (0-1) = 0 D(D-1) [o-2+ (+3)] = 0 D(0-0) (0 +0) = 0 => D=09197 Yg (X) = AX) + B(x)' + could GRO)= Woonskim Wegra ya 94 A+ Blo+cool y ye gill D W(X)= 2 X3 md

WIE 0 0 X X 0 2x3 1 x = -x + x² + x1 (-x) = -2 HgX) ti! 11 0 0 * 2 1(x) - 0 +x (0) = b to 0 4₂ (X) = Х 6 0 0 0 - ger) al llo) dx + 4e09 (zunan - 0967). + 1 HX) HelX) Ident YA NT "JUX) WE(X) = 1-X (0) - 0 = 1 ; gew= et Yp(x) = yif -'S. seniche.dk + x fc$ 0 --a peter) **[*] * * (42 ax goreng Yp(x) = yex) = A + Bxt Coulter 80 X Answer