华中师范大学常微分方程期末考试高分题库全集含答案.docx
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y''Ty'+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y''7y'+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（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*t'2C. s=-(1.2)*t2D. s=1.2g*t*2正确答案：C<9)函数y=cosx是卜列哪个微分方程的解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=25B. 3x+4y=CC. x2+y2=CD. x2+y'2=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<)A.可分离变量方程B.线性方程C.全微分方程D.贝努利方程正确答案：B(16)n阶线性非齐次微分方程的所有解O.A.构成一个线性空间B.构成一个联1维线性空间C.构成一个"1维线性空间D.不能构成一个线性空间正确答案：D(17)按照微分方程通解定义，y''=Sinx的通解是O.A. -sinx+C1.x+C2B. -sinx+C1.-KZ2C. sinx+C1.x+C2D. sinx+C1.-KZ2正确答案：A(18)微分方程2ydy-dx=0的通解为O.A. y2-=CB. y-'(1/2)=CC. y=x+CD. y=-+C正确答案：A(19)方程dydx=y-(1/2)+1()奇解.A.有一个B.有两个C.无D.有无数个正确答案：C(20)微分方程Xyy''+x(y'>3-y'4-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'''-<sup>2<sup>y,-<sup>5<sup>=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=x<sup>2<sup>C. y=-2xD. y=-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.e<sup>x<sup>B. e<sup>x<sp>1C. e<sup>x<sup>+1.D. 2-e<sup>x<sup>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=e<sup>x<sup>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.)=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:/itemb<.c11zyg1ptODTEMP202008260DmnzqxTEMP20200826012835124.p117Expires=1913779715feOSSccessKeyId=bI8DR1.k7JJh1.bEuSignature=uiaa3FBs76PIZ3BmC1.YIEwg0mkD->A. <imgi<1.=*ODedzayTEMI,20200826012837084.png"src=zyg1.ptODTEMP20200826ODedzayTEMP20200826012837084.png?Expires=19137797170SSAccessKeyId=gbI8DR1.k7JJh1.bEnASignature=hQv61hCPG2D11b5Pxkj7sc4I%3D*>B. <ingid=*0I)tqoupTEMP20200826012835436.png"src=*zyg1.pt0DTEMI7202008260DtqoupTEMP20200826012835436.png?EXPircs=1913779717½0SSAcccssKcyId=gbI8DR1.k7JJh1.bEnASignature=ETUar69Vm1.zvKg21IsQINeFVJZ0%3D*>C. <imid=*ODhibnzTEMP20200826012837375.png,rsrc-zy1.pt0DTEMP20200826ODhibnzTEMP20200826012837375.png?Expircs=1913779717A0SSAccessKcyId=gbI8DR1.k7JJh1.bEwASignaturc=YUfTKP7aPIsoXZx2yZySSP0sWk%3D,>D. <imgid=*,ODucznfTEMP20200826012837516.pngSrC=zyg1.ptODTEMP/2020/082601)wcznfTEMP20200826012837516.png?Expires=1.913779715&()SSAccessKeyId=gbI8I)Ri.k7JJhI.bEw&Signature=H4Hvr1.JQymBVkI.4sys3G1DfU3jTs%3I)>(31)下列函数中，为微分方程<imgid=*ODaizkcTEUP20200826012835968.png*src=-http:/Zitembankcdn.open,com,cnzyg1ptODTEMP202008260DaizkcTEMP20200826012835968.p117Expires=1913779717fcOSSccessKeyId=gbI8DR1.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.O¾2BdmOVSXI%3D/».A.<imgid="ODucssyTEMP20200826012836295.png”src=*http:/zyg1.pt0DTEM1720200826ODucssyTEMP20200826012836295.png?Expires=1913779716ftOSSAcccssKeyId=gbI8DR1.k7JJh1.bEw&Signaturc=tAa9iCkqQspzUv9Z1.DZtyjSRGY%3D*>B. <imgid=*,0)mzndTEMP20200826012836-151.src-,zy1.pt0DTEMP20200826(>D11zngdTEMP20200826012836151.Png?EXPires=1913779716i()SSAccessKeyId=gbI81.)R1.k7JJh1.b1.ASignature=GrdO2h6S6sQh1YbB23cJRGkWbus%3D>>C. <imgid=*,ODuypspTEMP20200826012836627.pngsrc=zyg1.pt0DTEMP20200826OIhypspTEMP20200826012836627.pnB?Expires=191377971640SSAccessKeyId=gbI8DR1.k7JJh1.bEw&Signature-9J(1.HrOREz%2BkKhKISzjFgIkr11><3D">I).<imgid=*OI)yhgiPTEMP20200826012838568.png"src=zyg1.pt0DTIMP20200826OI)yhgipTEMP2020O826012838568.png?Expires=1913779716ftOSSAccessKeyId=gbI8DR1.k7JJh1.bEnSSignature=Z23dpF7mN8x8THCBP6MwaZti7E%3D*>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.I95ADkaQo1.po(15Jb4zM%3D”/的解.A. <imgid=*ODbrdmxTEMP20200826012837016.pngsrc=httpzyR1.pt0DTEMP20200826ODbrd11xTEMP20200826012837016.png2Expires=1.913779717ftOSSAccessKeyI<1.=gbI81)R1.k7JJh1.b1.Signature=jDKzg43mTZi8cot4sZor6mBE4Ec%3D*>B. <imgid="ODXCaCaTEMP20200826012837193.png”src=*zyg1.pt0DTEMP/2020/0826/0DXeaeaTEMP20200826012837193.png?EXPires=1913779719&0SSAccessKeyId=gbI8DR1.k7JJh1.bEwSSignature=OcSxkFhVVX2W1dpcAvX36ocUmO%3D>C.<ingid="ODoeaZ1.TEMP20200826012837531.png”src=http:/Zzyg1.pt0DTEMP202008260DoeaztTEMP20200826012837531.png?Expircs=19137797190SScccssKeyId=gbI8DR1.k7JJh1.bEw&Signature=ts2S%2Bn8dhQI>zCav%2BnQQIgFGitE3D*>D.<imgid="ODpcxgiTEMP20200826012837718.png”src=*http:/itezyg1.ptODTEMR/2020/0826/0DpCXgiTEMP20200826012837718.png?Expircs=191377971740SSAcccssKcyId=gb!8DR1.k7JJh1.bEw&Signaturc=0OSsPYWn147k%2BrXwaH4Th3TPAo%3D,>正确答案：C(33)方程<imgid=,0DgzwatTEMP20200826012839652.png*"src="zyg1ptODTEMP/2020/0826/0DgZWatTEMP20200826012839652.pnK?Expires=1913779717&0SSAccessKeyId=gb1.8DR1.k7JJh1.bEw&Signature=v6kb/TmiY9e1.CGJ9867dbFiY2rg%3D”/的通解是()(<imgid=,()I)qjqdkTEMP20200826012839794.png,SrC="http:A.<imgid="ODdgyqqTEMP20200826012839989.png”src=*http:/itezyg1.pt0DTEM1720200826()DdgyqqTEMP20200826012839989.png?Expircs=191377972040SSAccessKcyId=gbI8DR1.k7JJh1.bE«&SignatUrC=9FVBWnSRTS98fEHIH0c/DafyPbO%3D”>B.<imgid=*,ODvzqxeTEMP20200826012838340.pngsrc-httpiIzyg1.ptODTEMP2020082601)vzqxeTEMP20200826012838340.png?Expires=1.913779720i0SSAccessKeyId=gbI«I)R1.k7JJh1.bEw&Signature=fVBYD6AVJnw1mX6zF110Q1.7ujU%3D>C. <imgid=*ODhxyvnTEMP20200826012838504.pngsrc=*zyg1.pt0DTEMP20200826ODhxyvnTEMP20200826012838504.png?EXPires=19137797200SSAccessKeyId=gb1.8DR1.k7JJh1.bEwSignature二UhB8FfJvZheppRSQqEcd3r5ecPo%3D*>I),<ingid=*OI)s11dasTEMP20200826012840448.png'src=*zyg1.pt0DTEMJ720200826ODsmdasTEMP20200826012840418.png?Expires=1.913779718&0SSAccessKeyId=gbI8DR1.k7JJh1.bEw&Signature=t11tuCPzGYycun1.7YeT1.K1.NBMcOE,3D>(34)下列微分方程中,可分离变量的是().A. <imgid=*ODsfibrTEMP20200826012840676.pngSrC="http:/iIzy1.pt00TEMP/2020/0826/ODsfibrTEMP20200826012840676.png?Expires=1.91377972240SSAccessKeyId=gbI8I)R1.k7JJh1.bE»&Signature=h41.1.YS2BFA7v0CvfmcTs1.C48T3k%3D,>B. <imgid=,ODkxxxiT三,20200826012842615.png*src="zyg1.ptODTEMP20200826ODkxxxiTEMP20200826012842615.png?EXPires=1913779722AoSSACCeSSKeyId=gb!8DR1.k7JJh1.bEw&SignatureTKUZakXgoy1.f1.GGXd6DzeRqM04k%3I)*>C. <ingid=,01)aegztTEMP20200826012842758.png'src=*httpzyg1.pt0DTEMJ7202008260DaogztTEMP20200826012842758.png?Expires=1913779722&0SSAccessKeyId=gbI8DR1.k7JJh1.bEw&Signature=ZZE4%2BR31.9QA6W6618VYY5WgjG8%3D”>D. <imgid=*ODevbdxTEMP20200826012843276.src=http正确答案：B(35)方程<imgid=,ODibfcEMP202008260128-13414.png*,src=,zyg1ptODTEMP20200826ODibfcEMP20200826012843414.pn7Expires=1913779721tOSSccessKeyId=gb1.8DR1.k7JJh1.bEuSignature6Yo11JI1.S8DP5M9g1.jZa>6C1.pu8iM%3D">()奇解.A.有一个B.有两个C.无D.有无数个正确答案：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. <imgid=*ODod1bvTEMP20200826012842058.png*src=*httpMs1VvrO2WcdceJ1.5Foe1.DNZzcU%3D*>B. <imgid=*ODgygoiTEAIP20200826012842216.png*src="zyg1.pt0DTEMP202008260I)gygoiTEMP20200826012842216.png?EXPires=1913779724A0SSAccessKeyId=gbI8DR1.k7JJh1.bEwASignature-JI1.mtfS4WAG%2BcIxnrrooNHiF0H%2BQ%3D*>C. <imgid=,01)o1rhiTEMI,20200826012844171.png”src=*http:/D. <ingid=,OI)xzgugTEMP2020D826012842519.png"src=*http:/itezyg1.pt0DTEM1720200826()DxzgugTEMP20200826012842519.png?Expircs=191377972240SSAcccssKcyId=gbI8DR1.k7JJh1.bE»&Signaturc=1.dat4TCq%2BQZEEufMenYT1.tnxb4m3D*>正确答案：C(40)微分方程Qmgid=0Ds1.dcwTEMP20200826012812669.png*src="h1.tp:/).<imgid=*ODrktzTEMP20200826012844598.png*src=8. <imgid=*ODbray1TEMP20200826012844764.png*src=*h11p:/C.<imgid="ODybbOPTEMP20200826012844940.png”src=*httpzyg1.j>t0DTEMI,20200826()I)ybbopTEMP20200826012814940.png?Expircs=1913779725&0SSAcccssKcyId=gbI8DR1.k7JJh1.bE»&Signaturc=0RdOerr8ShnMMftnsER%2BqvYtqZE%3D">D.<imgid=*ODfnihtTEMP20200826012843300.pngwsrc-,zy1.pt0DTEMP20200826(>Df11ihtTEMP20200826012843300.png?EXPires=19137797250SSAccessKeyId=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.k7JJh1.bEu&Signature=XWOrODdZ8jXfozIpg3zMu2Rna8I%3D”/».<imgid=*0DcxoycTEMP20200826012843788.png*src=*zyg1.pt0DTEMP202008260DexoycTEMP20200826012843788.png?EXPires=1913779723&0SSAccessKeyId=gbI8DR1.k7JJh1.bEnSSignature=SCfy7TIeE6r84uEt4t4ADA6pxk%3D*>B.<imgid=*OI)s1uigTEMP20200826012815732.png*SrC="http:zyg1.pt0DTEMJ720200826ODs1.uigTEMP20200826012845732.png?Expires=1913779721&0SSAccessKeyId=gbI8DR1.k7JJh1.bEw&Signature=«,Fj8f7Vw850S2xj1.knmdEuRBUnyM%3D">C.<imgid="ODekvwnTEMP20200826012844085.png”SrC="http:/zyg1.pt0DTEM1720200826()DekvwnTEMP20200826012844085.png7Expircs=1913779726OSSAccessKcyId=gbI8DR1.k7JJh1.bEwSignaturc=4zIFQnt9Rv¼2By1ZvWqQI9jhZzqv8%3D*>D.<imgid=*,ODImtyfTEMP20200826012846026.pngsrc-httpzyg1.ptODTEMP/2020/0826/ODImtyfTEMP20200826012846026.j)ng7Expires=1.913779726ftOSSAccessKeyId=gbI8I)R1.k7JJh1.bEwASignature=PYu6gIhHDu2qqz5hbWEDib81.Vvs%3D*>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="ODthprjTEMP20200826012846344.png”SrC="http:zyg1.pt0DTEMP202008260DthprjTEMP20200826012816344.png?Expircs=1913779726&0SSAcccssKcyId=gbI8DR1.k7JJh1.bEu&Signature=TNx2cXjb<ixH0f4Mq1.SOO92%2B0pg%3D*>.A. <imgid=*ODyjmbnTEMP20200826012846516.png*src=*http:/itebankcdn.oj>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
