Question

solve an ODE of whatever expression using ode45 in matlab obtaining the result [t,y]. Evaluate the solved ODE in a point. Everything should be done in matlab.

Answer 1

clc;
clear all;

%y'=-ty/sqrt(2-y^2), y(0)=1, t in [0,5]
f=@(t,y)-t.*y./(sqrt(2-y.^2));
tspan=[0,5];
y0=1;

[t,y1] = ode45(f , tspan, y0);
[t,y1]

%%%%%Solution

ans =

0 1.0000
0.1250 0.9922
0.2500 0.9697
0.3750 0.9342
0.5000 0.8881
0.6250 0.8341
0.7500 0.7747
0.8750 0.7120
1.0000 0.6478
1.1250 0.5836
1.2500 0.5208
1.3750 0.4602
1.5000 0.4027
1.6250 0.3489
1.7500 0.2994
1.8750 0.2543
2.0000 0.2137
2.1250 0.1778
2.2500 0.1463
2.3750 0.1192
2.5000 0.0961
2.6250 0.0765
2.7500 0.0603
2.8750 0.0470
3.0000 0.0363
3.1048 0.0290
3.2096 0.0229
3.3145 0.0180
3.4193 0.0140
3.5077 0.0113
3.5960 0.0090
3.6844 0.0072
3.7728 0.0057
3.8513 0.0046
3.9297 0.0037
4.0082 0.0030
4.0867 0.0024
4.1582 0.0019
4.2298 0.0016
4.3014 0.0013
4.3730 0.0010
4.4393 0.0008
4.5057 0.0007
4.5721 0.0005
4.6384 0.0004
4.7006 0.0004
4.7628 0.0003
4.8250 0.0002
4.8872 0.0002
4.9154 0.0002
4.9436 0.0002
4.9718 0.0001
5.0000 0.0001