常微分方程練習(xí)題(復(fù)習(xí)題)

常微分方程練習(xí)試卷一、x3d2x10dt2xdyf(xy)_______ydxd3yy2x0y(0)1,y(0)2dx3yyyexy*(x)e2xexxexW(t)0x1(t),x2(t),L,xn(t)axbxydx(2x23y220)dy0yA(t)X(t)A(t)20x'x05y2y5yy1y2yy0二、dyxy1dxxy32xdx(dx)20dt2dtyysinx(cosxsinxxy2)dxy(1x2)dy0A311dXdXAXx(0)241AX(t)dtdtdy2x13y2(1,0)dx(dy)34xydy8y20dxdxA21xAx(t),(0)1,142(t),(t)XA(t)XC(t)(t)C(x)(x0,x)x2y()y(x)y0[]d,x0,x[,]x0{n(x)}[,](x)[,][,](x)(x)(t)dXAX(t0)(t)expA(tt0)dtuxy1du1dx3,2,1u(f(u)1)xy31eAte2t0(t)(t)e5t0dyxy1dxxy3xy10,x1,y2x1,xy30y2,d(1z)dzd12d.z1z2arctanz2ln(1z)ln||Carctany2ln(x1)2(y2)2Cx1xd2x(dx)20dt2dtyysinxyyycexyc(x)exc(x)exc(x)exc(x)exsinxc(x)exsinxc(x)1ex(sinxcosx)cycex1(sinxcosx)22(cosxsinxxy2)dxy(1x2)dy0M(x,y)cosxsinxxy2,N(x,y)y(1x2)M2xyNyxcosxsinxdx(xy2dxyx2dy)ydy0d(1sin2x)d(1x2y2)d(1y2)0sin2xx2y2y2C222A311dXAX(t)dXAXx(0)241dtdtdet(AE)31(2)(5)0,242,512,5V11,V21,(,0).12212(t)e2te5t.1(0)121e2t2e5t113(t)(t)11e2te5t2111e(0)2t2e5t1113e3e

tt

2e4e

5t5tdy22x13y(1,0)0(x)0x02(x)]dxx21(x)y0[2x13x,1x1312(x)]dx1xx2x33x43x5,2(x)y0[2x11025(dy)3dy8y20dx4xydxdy38y2xdxp38y24ydydypx4ypdxdx34y2)dpp(8y2p3)4y2p2y(pdy(p34y2)(2ydpp)02ydp1p2c2dydyp0pcy2y(c)2pxc24xc22p4c2(p)2c143p34y20p(4y2)3y27xA21xAx(t),(0)1,142p()2126903n1141,221v(t)3t1ti3E)i13t1t(12)e(Ae2)2i0i!22t(1etn1ti(AE)ii0i!3tEt(A3E)3t10113t1ttexpAtee01t1e1t1t(t),(t)XA(t)XC(t)(t)C(t)1(t)X(t)1(t)(t)X(t)detX(t)0(t)(t)X(t)(t)(t)X(t)(t)X(t)A(t)(t)X(t)(t)X(t)A(t)(t)(t)X(t)(t)A(t)(t)(t)X(t)0X(t)0,X(t)C(t)(t)C(x)(x0,x)x2y()y(x)y0[]d,x0,x[,]x0{n(x)}[,](x)[,][,](x)(x)x(x)y0[2()]d,x0x0(x)y0,n(x)y0[2n1()]d,x0,x[,](n1,2,)x0x0xxx0x2max{x2|(x)0(x)|(|()|||)dM(xx0),M|(x)||x|}x0x[,]xxML(xx0)2,|(x)1(x)|(2|()0()|)dLM(x0)dx0x02!Lmax{x2}n|(x)1(x)|MLn1nnn!(xx0)x[,]x2xMLn1MLn|(x)n(x)|(|()()|)dL(x0)nd(xx0)n1,n1x0n!(n1)!x0k|(x)k1(x)|MLk1(xx0)kMLk1()kk!k!k0{n(x)}x0x(x)(x)(x)x0x(t)dXAX(t0)(t)expA