Question

Constr d a second order problem of a inar sion and an exponenti al ksm r plan before up

Answer 1

Solution Given tha The gereral omoSerord oder DE tcorelant Coefficients ond a excing unconf the frm Construct a Secard oider problem of this -ype ty choosing a,b.ceR Call ㎜ zero) and flt) &ch tht fet) is a treaY combination of the Sine ard casine furnc-Hiors Step-l choose a,bic eR such that talt e ron-zero) fox the chasoctesstic equation a+brtc :o sbeoee voots ate eal and disltne co veal and ereated

2 is not a ot of the chavaclerstic equad ion Then the Second order will be Ecample {좋 alto 2. Example 2 C2 25 ệt, construct aSecond oder pooblem 아 thisHjpe by crosm abc, e R Call ron zeto) ard a forcingfunction that is the sum of lirear equation ond an exarental em

3 Step choose the Real umbats ab.c such thd of att are oil hate a sltable choractertstic eqution Step 2 Bis a linear equadion and et is an exponental Function Example 3 The ereral Soletion of +he Gecond oder ren homgenets tinear equadion constant Coefficients arttb ft) can be expessed in

Here. Xp Lt) →Non-tong-rous Solution xclt), GXAcA, ( χι Ђ. ave a pair of fardamental Solutions ol the conrespondling homcgeneaus General Soluhion up posi then for any pair of abioy constatsand te