一类二阶常系数非齐次线性微分方程的特解求法.pdf

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1、STUDIES IN COLLEGE MATHEMATICSVol.24,No.3May 2021doi10.3969/j.issn.1008-1399.2021.03.014362000nG642,O175.1 A 1008-1399(2021)03-0047-03Particular Solution of a Class of Second Order Constant Coefficient Non-homogeneous Linear Differential EquationsHUANG Liwen(College of Mathematics and Computer scien

2、ce,Quanzhou Normal University,Quanzhou 362000,PRC)Abstract With an examplethis paper discusses two methods presented in the textbook for particular solutions of second-order constant coefficient non-homogeneous linear differential equations,and introduces a relatCvelysCmplemethod.Keywords second ord

3、er linear differential equation,particular solution,non-homogeneous0*+:*+*f().(1)f)eP(f()e Pz()cos+Q”sinf(f(1)2)2020-05-12 2020-08-12(JR201801.(1979 ),.Email,*.1 f()=eP”1)*7()=2”e1)2”k 0 k=1 2 H(=2”*7()=H()eH(+(2+)H,(+(A+p+q)H(P”*H4820215*(kR”(H(H(*(H(.1)r1+pr+q=0.(3)3)r1,n.r1,n*()=kR(eHH(=kR(H2)1H(

4、+p)H(+p+q)H(=P”(2H(+p)H(=P(3H(=P”R(1*6*9*=(+1)er6r+9=0r1=r2=3=3*7=a+6H(=(a+6=a+6H=3a+26H=6a+262)6a+26=+1 a=6=2*=a+6H(=a#+6cox+Xf(=e Pz()co+Q”sin1)*7(.)=kRc()cos+R!)()sire(4k,R(Rm=max2,”i(i)k0+i(i)=1f(f()4)f(=eP(.et+_1 et e_tcos=2 sin=2 f(qi|Q_i ai a_if=e PO +QM=P+Q“e+1+P Q”_-1L 2 T 2iL 2 2i=Rm()e +R

5、m(eR(Rmm=max-/*1*+p*+q*=Rm()e (5)5D+p*+q*=Rm()e(=Rm)e(_*4+p*+q*=Rm()e(=Rm()e(7)*7(=*(+*(D=*+*=*+*=*24349*()2Re(*()(8)*+*+q*=e P()cos+Q”sin 5)8)f(42*+4*+5*=(5+4z+3)ecos2.=2,25)/+4*/+5*=e(9)9)E+4+5 0,1,2 2fif=2+2i*=($+6+c+d)e(H=$3+62+c+KJH=3$+26+c H()=6$+26(2)6$+26+(2+21)+4(3$+2 6+c)+(2+2 i)2+4(2+2 i)

6、+5($+6+c+K)5+4+3=2 3$+1$i36)+6$+86i3c)+5+4+3(2 6+4f3K)3=53$=21$i36=6$+86i3c=032 6+4ci 3K=5 1!$i!10i$=66=3 6$+86i 6516ic3J6ci 3=77+400iK=3=9)2+10i 2 6516i-TT3 9,77+400i.2+i54 5 3 2+10i,65 161+-6 3 9+)e2(cos2+isin2)54=(+cos26 3 9 54+3+9 5)sin2(3 9 54+i3+9 50cos23 9 548)*$)=2Re$*1$)+22400 27)sin2(e!*()=e$+61+c+K)cos2+($+6+c+K)sin2(*($,6,c,K,(=1,2).2!31(M(.7,2015.2(J(.2016(5):99-100.3(”J(.2010,13(3):57-58.4(.J(.2000,18(4):339-343.