PDF-2(6)+(7)+(8))y00+y0+y=e2xf( 5+4+1)sin3x+(12+6)cos3xg=18cos3xAssignment
Author : tawny-fly | Published Date : 2016-07-27
2cosxy009y4cosx3ysinxcosxexy0y2cosx4y3e2x4exy003y02y05ytsin2ty004y4cos2t6y5xe4xy008y016y07ye3xsin2xy005y12e3xcos2xApplicationsofdi erentialequations
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2(6)+(7)+(8))y00+y0+y=e2xf( 5+4+1)sin3x+(12+6)cos3xg=18cos3xAssignment: Transcript
2cosxy009y4cosx3ysinxcosxexy0y2cosx4y3e2x4exy003y02y05ytsin2ty004y4cos2t6y5xe4xy008y016y07ye3xsin2xy005y12e3xcos2xApplicationsofdi erentialequations. y2+2x3=C3ReduciblesecondorderODEAgeneral2ndorderODEisoftheformF(x;y;y0;y00)=0Insomecases,bymakingsubstitution,wecanreducethis2ndorderODEtoa1storderODE.FewcasesaredescribedbelowCaseI:Iftheindependentva b2 4ac 2a(32)Thesolutionof(29)isgivenby:RealRoots(r16=r2):yh=C1er1t+C2er2t(33)Repeated(r1=r2):yh=(C1+C2t)er1t(34)Complex(r= i ):yH=e t(C1cos t+C2sin t)(35)Thesolutionof(30)isy=yp+yhwhereyhisgivenby(3 ThisisachapteroftheStacksProjectversionfac02ecdcompiledonSep1420211DERIVEDCATEGORIES239Admissiblesubcategories11240Postnikovsystems11441Essentiallyconstantsystems11942Otherchapters121References1221Int 25 Inthischapter,weexplorehowtheLaplacetransforminteractswiththebasicoperatorsofcalculus:differentiationandintegration.Thegreatestinterestwillbeinthe rstidentitythatwewillderive.Thisrelatesthetransfor
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