solve an ODE of whatever expression using ode45 in matlab obtaining the result [t,y]. Evaluate the...

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Advance Math

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

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4.3 Ratings (783 Votes)

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

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