MATALAB基礎(chǔ)知識(shí)微分方程

1、實(shí)驗(yàn)五1、求下列微分方程的解析解。2 dyx -dxy xy=2 兀一3加+ 3e=4不一號(hào)+3z=4x-+2(1) 、dsolve('Dy=(y-x*y)/(xA2)','x')ans =C1/exp(1/x)/x(2) 、x,y,z=dsolve('Dx=2*x-3*y+3*z','Dy=4*x-5*y+3*z','Dz=4*x-4*y+2*z','t')x =C1*exp(-t)+C3*exp(2*t)y =C1*exp(-t)+C2*exp(-2*t)+C3*exp(2*t)z =C2*ex

2、p(-2*t)+C3*exp(2*t)I IIXI2、求微分方程x x 2e t,x(0)1,x (0)2的數(shù)值解。y仁 x,y2=y1 'y1' y2y2' 2e t t y2y1(0) 1,y2(0)2先建立M文件：fun cti on f=cxd(t,y)f=y(2);2*exp(-t)+t-y(2)在輸入指令：T, Y=ode15s('cxd',0,3000,1,-2);plot(T, Y(:,1),'-')f =-244.543.532.521.510.506x 100500100015002000250030003、實(shí)驗(yàn)內(nèi)容狼

3、追擊兔子問題狼追擊兔子問題是歐洲文藝復(fù)興時(shí)代的著名人物達(dá).芬奇提出的一個(gè) 數(shù)學(xué)問題。當(dāng)一個(gè)兔子正在它的洞穴南面60碼處覓食時(shí)，一只惡狼出現(xiàn)在兔子正東的100碼處。當(dāng)兩只動(dòng)物同時(shí)發(fā)現(xiàn)對(duì)方以后，兔子奔向自己的洞 穴，狼以快于兔子一倍的速度緊追兔子不放。狼在追趕過程中所形成的軌 跡就是追擊曲線。狼是否會(huì)在兔子跑回洞穴之前追趕上兔子？實(shí)驗(yàn)要求：1.寫出數(shù)學(xué)模型；2 .利用ode45命令求出微分方程數(shù)值解；>> tspa n=100:-0.1:0.1; yo=o 0;T,Y = ode45('fu n',tspa n,y0);n=size(Y,1);disp('狼的坐

4、標(biāo)(x=0.1)')disp(Y( n,1)狼的坐標(biāo)(x=0.1)63.50073. 進(jìn)行結(jié)果分析。通過上面運(yùn)行結(jié)果可知，狼并沒有追上兔子。4、 某人從銀行貸款購(gòu)房，若他今年初貸款10萬元，月利率0.5%，每月還1000元，建立差分方程計(jì)算他每年末欠銀行多少錢，多少時(shí)間才能還清？ 如果要10年還清，每月需還多少？fun cti on x=exf11(x0 ,n ,r,b)a=1+r;x=x0;for k=1: nx(k+1)=a*x(k)+b;endk=(1:140);y=exf11(100000,140,.0005,-1000) x0=100000;r=0.005;n=120;b=-

5、r*xO*(1+r)4 n/1-(1+r)4 ny =1.Oe+OO5 *Columns 1 through 111.OOOOO.99O5O.981OO.9715O.962OO.9525O.9429O.9334O.9239O.9143O.9O48Columns 12 through 22O.8952O.8857O.8761O.8666O.857OO.8474O.8379O.8283O.8187O.8O91O.7995Columns 23 through 33O.7899O.78O3O.77O7O.7611O.7515O.7418O.7322O.7226O.7129O.7O33O.6936Col

6、umns 34 through 44O.684OO.6743O.6647O.655OO.6453O.6356O.626OO.6163O.6O66O.5969O.5872Columns 45 through 55O.5775O.5678O.558OO.5483O.5386O.5289O.5191O.5O94O.4996O.4899O.48O1Columns 56 through 66O.47O4O.46O6O.45O8O.4411O.4313O.4215O.4117O.4O19O.3921O.3823O.3725Columns 67 through 77O.3627O.3529O.3431O.3

7、332O.3234O.3136O.3O37O.2939O.284OO.2742O.2643Columns 78 through 880.2544 0.24460.23470.22480.21490.20500.19510.1852 0.1753 0.16540.1555Columns 89 through 990.1456 0.13560.12570.11580.10580.09590.08590.0760 0.0660 0.05600.0461Columns 100 through 1100.0361 0.0261 0.01610.0439 -0.0539 -0.06400.0061-0.0

8、039-0.0139-0.0239-0.0339Columns 111 through 121-0.0740 -0.0840 -0.09410.1544 -0.1645 -0.1746-0.1041-0.1142-0.1242-0.1343-0.1444Columns 122 through 132-0.1847 -0.1948 -0.20490.2656 -0.2757 -0.2858-0.2150-0.2251-0.2352-0.2453-0.2554Columns 133 through 141-0.2960 -0.3061 -0.3163-0.3264-0.3366-0.3468-0.3569-0.3671-0.3773 b =1.1102e+00315、試用不同的算法計(jì)算定積分01x(1 x2)dx 的數(shù)值解。梯形積分法：x=0:1;y