Part1OrdinaryDifferentialEquations(常微分方程式微分变数只有一个)

发布时间：2023-02-03 09:06:37

Chapter1First-OrderODEsCChhaapptteerr22SSeeccoonndd--OOrrddeerrLLiinneeaarrOODDEEss((二二階階線線性性常常微微分分方方程程式式Chapter3Higher-OrderLinearODEsChapter5SeriesSolutionsofODEsChapter6LaplaceTransforms‧Ordinarydifferentialequationsmaybedividedintotwolargeclasses,linear(線性andnonlinear(非線性ODEs.WherenonlinearODEsaredifficulttosolve,linearODEsaremuchsimplerbecausetherearestandardmethodsforsolvingmanyoftheseequations.22..11HHoommooggeenneeoouussLLiinneeaarrOODDEEssooffSSeeccoonnddOOrrddeerr((二二階階線線性性齊齊性性微微分分方方程程式式‧Asecond-orderODEiscalledlinear(線性的ifitcanbewrittenasyp(xyq(xyr(x.(1線性：方程式的每一項都不得出現y(x和其導數(y,y,…的乘積或自乘Incaser(x0,theequationiscalledhomogeneous(齊性的.Incaser(x0,theequationiscallednonhomogeneous(非齊性的.Thefunctionsp(xandq(xarecalledthecoefficientsoftheODEs.‧Theorem1SuperpositionPrinciplefortheHomogeneousLinearODE(適用於線性齊性常微分方程式的疊加原理Ifbothy1(xandy2(xaresolutionsofthehomogeneouslinearODEyp(xyq(xy0,(2thenalinearcombination(線性組合ofy1andy2,sayc1y1(xc2y2(x,isalsoasolutionofthedifferentialequation.Proof–-19-
Lety1andy2besolutionsofequation(2.Itmeansthatpy2qy20.py1qy10andy2y1Thenbysubstitutingyc1y1c2y2into(2,wegetypyqy(c1y1c2y2p(c1y1c2y2q(c1y1c2y2c2y2p(c1y1c2y2q(c1y1c2y2c1y1py1qy1c2(y2py2qy2c1(y10Thisshowsthatc1y1c2y2isasolutionof(2.Example1AHomogeneousLinearODE(線性齊性微分方程式Example2ANonhomogeneousLinearODE(線性非齊性微分方程式Example3AhomogeneousNonlinearODE(非線性齊性微分方程式-20-

Part1OrdinaryDifferentialEquations(常微分方程式微分变数只有一个)

推荐内容

相关推荐