数学实验报告-6new

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1、《数学实验》报告实验名称  常微分方程的求解学院材料科学与工程专业班级     姓  名    学  号      6  2014年5月6一、【实验目的】掌握常微分方程求解和曲线拟合的方法，通过MATLAB求解一阶甚至是二阶以上的高阶微分方程。二、【实验任务】P168习题24，习题27三、【实验程序】习题24：dsolve('Dy=x*sin(x)/cos(y)','x')习题27：functionxdot=exf(t,x)u=1-2*t;xdot=[0,1;1,-t]*x+[01]'*u;clf;t0=0;tf=pi;x0t=[0.1;0.2

2、];[t,x]=ode23('exf',[t0,tf],x0t)y=x(:,1);Dy=x(:,2);plot(t,y,'-',t,Dy,'o')四、【实验结果】习题24：ans=-asin(-sin(x)+x*cos(x)-C1)习题27：t=00.0145454545454550.0872727272727270.2014401138854870.32587561477274660.4621081545257860.6120588845946970.7778209505964080.9621414142264681.148168188604

3、6421.2767256120862191.4052830355677961.5188370165955031.6706032867795981.8601224103746342.0890844252498192.3568840673514062.6545701240972872.9687293894562673.141592653589793x=0.1000000000000000.2000000000000000.1030244246471320.2157878767999930.1214182230324930.2882738638067

4、500.1598075714380230.3798080186929570.2116371693411580.4479187112052590.2755877924969260.4847128501418690.3485406042644110.48126308828551960.4245498506176260.4281952199916280.4939245199515710.3168118938813220.5388257030793950.1599185464384220.5513032758270800.032044152168938

5、0.546590550593747-0.1069096721695130.527179289808037-0.2357757982034920.478030445443925-0.4127197193267390.378815910001838-0.6346766466560780.203655620089869-0.895157050243270-0.074213983594980-1.179711556163266-0.467733619239173-1.464563001247023-0.969131569806455-1.7289762

6、25937048-1.279254945443604-1.8585925457363346一、【实验总结】本次试验主要练习了常微分方程的符号解法和数值解法，并借助于矩阵通过一阶微分方程延伸至二阶微分方程的求解，同时还联系了前面的二维曲线绘图，综合性较强。6