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1、35099华中和范大学常微分方程期末符考题库35099奥期期末考试咫库含集单选题：(1)下列函数中，是微分方程yTy+12y=0的解()。A. y=x3B. y=x2C. y=e(3x)D. y=e*(2x)正确答案：C(2)微分方程y7y+4y=0的两个线性无关解是O.A. e(2x)与2e(2x)B. e(-2x)与xe(-2x)C. e(2x)与xe(2x)D. (-2x)4e(-2x)正确答案：C(3) y+sinxy-X=CoSX的通解中应含O个独立常数。A. 1B. 2C. 3D. 4正确答案：C(4) 一个不可延展解的存在在区间一定是O区间.A.开B.闭C.正D.负正确答案：A（
2、5）卜列函数中，哪个是微分方程dy-2xdx=0的解O.A. y=2xB. y=2C. y=-2xD. y=-正确答案：B（6）微分方程COSydy=SinXdX的通解是）,A. sinx+cosx=CB. cosy-sinx=CC. Cosx-Siny=CD. CoSX+siny=C正确答案：D（7）方程xy+y=3的通解是O.A. y=Cx+3B. y=3x+CC. y=-C-3D. y=C-3正确答案：A(8)下列函数中,哪个函数是微分方程s(t)=-g的解()A. s=-gtB. s=-g*t2C. s=-(1.2)*t2D. s=1.2g*t*2正确答案：C9)函数y=cosx是卜列
3、哪个微分方程的解O,A. y,+y=0B. y,+2y=0.yn+y=0D.y+y=cosx正确答案：C(10)方程dydx=(3)+y满足初值问遗解存在且唯一定理条件的区域是OA.上半平面B. XOy平面.下半平面D.除y轴外的全平面正确答案：D(I1.)方程组dYdx=F(x,Y),xR,YWR，的任何一个解的图象是O维空间中的一条枳分曲线.C. n+1D. n-1.E. n-2正确答案：B(12)微分方程dyd-x*y=O的通解是y=O.A. C/xB. CxC. 1/x+CD. x+C正确答案：B(13)微分方程dxy+dyx=O满足当x=3时，y=4的特解是O.A. x2+y2=25
4、B. 3x+4y=CC. x2+y2=CD. x2+y2=7正确答案：A（14）一阶微分方程的通解的图像是（）维空间上的一族曲线.A. 1B. 2C. 3D. 4(15)微分方程y1.nydx+(xTny)dy=O是3-y4-y=0的阶数是O,A. 3B. 4C. 5D. 2正确答案：D(21)y+y-2y=0是O阶常系数齐次线性微分方程“C.三D.四正确答案：B（22）微分方程y-2y,-5=1.的通解中应含的独立常数的个数为（）。A. 3B. 5C. 4D. 2正确答案：A（23）下列函数中，哪个是微分方程dy-2xdx=0的解（）.A. y=2xB. Y=x2C. y=-2xD. y=-
5、X正确答案：B（24）下列微分方程中,（）是二阶常系数齐次线性微分方程.A. y,-2y=0B. y,-xy+3y=0C. 5y,-Ix=OD. y,-2y+1=0正确答案：A（25）微分方程y-y=O满足初始条件y（0）=1.的特解为（）。A.exB. ex1C. ex+1.D. 2-ex正确答案：A(26)在下列函数中，能够是微分方程y+y=O的解的函数是(?A. y=1.B. y=xC. y=sinxD. y=ex正确答案：C(27)过点(1,3)且切线斜率为2x的曲线方程y=y(x)应满足的关系是(.A. y,=2xB. y=2x.y,=2x,y(1.)=3D.y,=2x,y(1.)=
6、3正确答案：C(2)微分方程imgid=ODqretkTIMP20200826012829850.png*src=*).A. 3B. 4D.2正确答案：D(29)微分方程Egid=*ODqcznkTEMP20200826012833613.pngsrc=h1.1.p:/itemb.c11zyg1ptODTEMP202008260DqeznkTEMP20200826012833613.pnK?Expires=1913779713&OSSAccessKeyId=BbI8DR1.k7JJh1.bEw&Signature=Kx2OS15(iWC5o4HZ6uU9VFViC0qE3D*/是().A. 一
7、阶线性方程B. 一阶非线性方程C.二阶线性方程D.二阶非线性方程正确答案：B(30)imgid=*,ODmnzqxTEMIj20200826012835124.png*src=http:/itembA. imgiB. C. D. (31)下列函数中，为微分方程imgid=*ODaizkcTEUP20200826012835968.png*src=-http:/Zitembankcdn.open,com,cnzyg1ptODTEMP202008260DaizkcTEMP20200826012835968.p117Expires=1913779717fcOSSccessKeyId=gbI8DR1.
8、k7JJh1.bEwSignature-XXIune2PZACb2U1.41.q7sjDfn0ow%3D”/的通解是()(ingid=*01)ukqdzTEMP20200826012837933.png*SrC=http:iIzyg1.ptODTEMP20200826ODukqdzTEMP20200826012837933.Png?Expires=1913779716&OSSAccessKeyId=gbI8DR1.k7JJh1.bEw&Signature=DdtJba5Kr2XsReOsN1.O2BdmOVSXI%3D/.A.B. D11zngdTEMP20200826012836151.Pn
9、g?EXPires=1913779716i()SSAccessKeyId=gbI81.)R1.k7JJh1.b1.ASignature=GrdO2h6S6sQh1YbB23cJRGkWbus%3DC. I).正确答案：B(32)卜列函数中，()是微分方程imgid=ODtmCjjTEMP20200826012838700.png.src=*httpzyg1.ptODEMP202008260DtmcjjTEMP20200826012838700.png?Expircs=1913779717fcOSSAcccssKcyId=gb18DR1.k7JJh1.bEw&Signature=bY8DTAm1
10、.I95ADkaQo1.po(15Jb4zM%3D”/的解.A. imgid=*ODbrdmxTEMP20200826012837016.pngsrc=httpzyR1.pt0DTEMP20200826ODbrd11xTEMP20200826012837016.png2Expires=1.913779717ftOSSAccessKeyIB. C.zCav%2BnQQIgFGitE3D*D.正确答案：C(33)方程imgid=,0DgzwatTEMP20200826012839652.png*src=zyg1ptODTEMP/2020/0826/0DgZWatTEMP20200826012839
11、652.pnK?Expires=1913779717&0SSAccessKeyId=gb1.8DR1.k7JJh1.bEw&Signature=v6kb/TmiY9e1.CGJ9867dbFiY2rg%3D”/的通解是()(imgid=,()I)qjqdkTEMP20200826012839794.png,SrC=http:A.B.C. I),(34)下列微分方程中,可分离变量的是().A. B. C. D. imgid=*ODevbdxTEMP20200826012843276.src=http正确答案：B(35)方程6C1.pu8iM%3D()奇解.A.有一个B.有两个C.无D.有无数个正
12、确答案：C(36)n阶线性齐次微分方程基本解组中解的个数恰好有1)个.B. n-1.C. n+1D. n+2正确答案：A（37）方程Gmfiid=,0DsvyfTEMP20200826012843574.png,rsrc=*http:/itebankcdn.open.Czyg1.ptODTEMP/2020/0826/0DSVyfgTEMp20200826012843574.png?EXPirCS=I913779723&0SSRCC。SSKCy1.d=gbI8DR1.k7JJh【.bEw&Signature=/GVvRZOmFVCCeNJkQ9pSeBb3y483D满足初值问题解的存在且唯一定理
13、条件的区域是（）.A.上半平面8. imgid=*ODvwngTEMP20200826012813711.png*src-*http:/iIembankcdn.open.COTC.下半平面D.除Y轴外的全平面正确答案：D（38）一个不可延展解的存在区间一定是（）区间.A.开B.闭C.左开右闭D.左闭右开正确答案：A（39）下列方程中，不是全微分方程的为（）.A. B. C. imgid=,01)o1rhiTEMI,20200826012844171.png”src=*http:/D. 正确答案：C(40)微分方程Qmgid=0Ds1.dcwTEMP20200826012812669.png*s
14、rc=h1.tp:/).imgid=*ODrktzTEMP20200826012844598.png*src=8. imgid=*ODbray1TEMP20200826012844764.png*src=*h11p:/C.t0DTEMI,20200826()I)ybbopTEMP20200826012814940.png?Expircs=1913779725&0SSAcccssKcyId=gbI8DR1.k7JJh1.bE&Signaturc=0RdOerr8ShnMMftnsER%2BqvYtqZE%3DD.Df11ihtTEMP20200826012843300.png?EXPires=1
15、9137797250SSAccessKeyId=gbI8DR1.k7JJh1.bEwSSignature=CJ5pb4CS3PE7orj%2BXrP1.uYG1.uHk%3D*正确答案：D(41)微分方程imgid=ODudyhuTIMP20200826012845247.p11-src=,http)(imgid=*OD1whhaT三,2020082601.2843632.png*src=zyg1ptODTEMP202008260D1.whhaTEMP20200826012813632.png?Expii-es=1913779723fcOSSAccessKeyId=gbI8I)R1.k7JJh
16、1.bEu&Signature=XWOrODdZ8jXfozIpg3zMu2Rna8I%3D”/.B.C.D.正确答案：B(42)微分方程imgid=0DcxgzmTEMP20200826012846174.pngSrC=http:zyg1ptODTEMP202008260DexgzmTEMP20200826012846174.png?Expires=1913779726feOSSAccessKeyId=gb18DR1.k7JJh1.bEuSSignature=oC11.Jx4eIiQISknKiOmCfgVnXgJg%3D/的通解为()imid=ODthprjTEMP202008260128
17、46344.png”SrC=http:zyg1.pt0DTEMP202008260DthprjTEMP20200826012816344.png?Expircs=1913779726&0SSAcccssKcyId=gbI8DR1.k7JJh1.bEu&Signature=TNx2cXjb.A. zyg1.pt0DTEMP20200826ODyjmbnTHMP20200826012816516.png?Expires=1.913779726&OSSAccessKeyId=gbI8I)R1.k7JJh1.bEw&Signature1.4MBbKIk6Q7IZ81.7qGJv8vVzQY%3D*B. imgid=*ODbyadkTEMP20200826012846658.png*src=zyg1.pt0DTEMP20200826ODbyadkTEMP2020O826012846658.pnB?Expires=1913779
