Wiley signals and systems e book TLFe BO 141

126 7.Solving liritial Condition Prohlems will1 the 1,aplace 'liarisf-orm lsl Classical The starting point tor the classical soliitiou to tht probleni cicscribecl tlbove consi ot calculating t lic sohition of tlic lioniogenous piohlern a i d of a particular soluti of tlw non-homogcrioi~~ problern A gcrirral solution is lorined faorri tlrr b n i m of tlic tao, in wl-iic*lithe pz cvioiisly open pararnetrrs are cMncd, so that tlir soliit ion lulfills the initial contlitions T l r ~follownig rxriniplc shows this classical soli11ion tor ilfirbl-order sy The liomogeiious solution yfL(t) mist fulfil1 t ~diffcvritial cquation r?)!,( t ) 2yfr(f= ) and in this case it i s \Tit11 the c.omplcx aiiiplitudc I' riot yet deteriniiic~d.hisert iiig iitt,o (7.2) yields I-