Can someone please explain to me how to use the reduction order formula for numb
ID: 2883115 • Letter: C
Question
Can someone please explain to me how to use the reduction order formula for number 6?
919% Wed 12:39 AM E Chrome File Edit View History Bookmarks People Window Help Differential Equations 4.2 x C chegg study I Guided solutio Twitter YUUK M c Secure https:/ Responses/submit?depa15355652 Your Da Apps YouTube H Netflix Other Bookmarks Songs Albums 6. -1 points ZillDiffEQModAp 10 4.2.011 My Notes Ask Your Teacher The indicated function y1(x) s a solution of the given differential equation. Use reduction of order or formula (S) in Section 4.2 Artists P(x) dx Stations yi(x) dx 5) y (x) Local F as instructed, to find a second solution y20x). yi n X PLAY L Discove Khalid Need Help? Read t Talk to a Tutor Parked Drake Submit Answer Save Progress 7. -1 points ZillDitTEQModAp10 4.2.013. My Notes Ask Your Teacher The indicated function yi(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2 r P(x) dx y1(x) dx (5 y (x) as instructed, to find a second solution y20x). xy 26y x cos (5 n X Need Help? Read it Talk to a Tutor All Night Chance TExplanation / Answer
6) we have given xy''+y'=0,y1=ln(x)
y''+(1/x)y'=0
comparing by y''+p(x)y'+q(x)y=0 for given equation
p(x)=1/x
eintegration of (-p(x)dx)=eintegration of (-1/xdx)=eln(x)=x
y2=y1(x)* integration of (eintegration of (-p(x)dx)/y21(x))dx
y2=ln(x)* integration of (x/(lnx)2)dx
y2= integration of (x/ln(x))dx
Apply integral substitution, u=ln(x),du=(1/x)dx,dx=xdu and x^2=e^(2u)
y2= integration of (x/ln(x))dx= integration of (e^(2u)/u)du
Apply integral substitution ,v=2u,dv=2du and u=v/2
y2= integration of (x/ln(x))dx= integration of (e^(2u)/u)du
=integration of (ev/v/2)(dv/2)=integration of(ev/v)dv
use the common integral integration of(ev/v)dv=Ei(v)
y2= integration of (x/ln(x))dx =Ei(v)+C
set back v=2u=2*(ln(x))
y2= integration of (x/ln(x))dx =Ei(2u)=Ei(2ln(x))+C
y2=Ei(2ln(x))+C