用MATLAB解常微分方程y'=-2xy,0<x<3,y(0)=1计算解析解和数值解

【1】解析解
>>y=dsolve('Dy=-2*t*y','y(0)=1')

y = exp(-t^2)

【2】数值解

function numeric
clear;clc;
[t,y]=ode45(@fun,[0 3],1)
plot(t,y,'*',t,exp(-t.^2))%*为数值解，线段为解析解
function yhat=fun(t,y)
yhat=-2*t*y

结果：
t =

0
0.0750
0.1500
0.2250
0.3000
0.3750
0.4500
0.5250
0.6000
0.6750
0.7500
0.8250
0.9000
0.9750
1.0500
1.1250
1.2000
1.2750
1.3500
1.4250
1.5000
1.5750
1.6500
1.7250
1.8000
1.8619
1.9237
1.9856
2.0475
2.0996
2.1517
2.2039
2.2560
2.3023
2.3487
2.3950
2.4414
2.4837
2.5261
2.5684
2.6107
2.6500
2