Question

part A

The indicated function y(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-SP(x) dx Y2 = Y1(x) dx (5) as instructed, to find a second solution 72(x). xy" + y' = 0; Y1 = In x Y2 =

part B

part C

Kindly show the detailed solution for reviewer! I'll rate it for sure thanks!

Answer 1

Coli Part A 0 Given: xy"+y's Inx -speada e dx Use y, a s 9,9 (S) Compare the ginen differential equation with P(x) y' + Q(x) y = f() gives P(s) = - x unre P(x) dx th I da - Spax -tnt pent x = e e-$260) dx dx f xt de (Ins² you at Put enx = t t dre dt xndx (Inse) ² t² = + -2+1 2+1 JI ㅗ t .L inse

ense x-1 Ye Inn Thus Y , Soli Past B cosha Ginen y" - y y, 0 Pla=o -SP(x) dx -foda e espe e - Spesiast da. dx ܕܡܢ (cash x)? da extex 2 4 da (extp-x 2 4 + e 2x = dx (12x+12 Put e 2x+1=t > 2 e 2x = dt dx f - Pxdy dx e dt 4 2 y²x) 11 - 2+1 2 t - 2+1 = -1 - - 2 t

2 e2x + 1 Thus coshx x - 2 Yz e 2n +1 2 X - Cashr x excet ex (AS "As Casha = ente center) losha en Coshx eare Thus enne ya soli Part C Given! (1-w' you + any y" + y' 1-x² P(s) 2x I-8² P(x)da 2x da Put 1-x²=t -2x - dt dx - ant .- Ln(1-x²) Plagda dt t

3 K-X स = Ac Thus M x - 11-he नो 12 त AP (X- --- म न म (-)-ने- xp(-of- Date

Answer 2

whoever did part c did not do it correctly!