Question

Solve the initial value problem dt y+e' a. Use ode45() to find the approximate values of the solution at 1-0,1,1.8,2.1 and also plot the solution. Now plot the numerical solution of several large intervals and make a guess about the nature of the solution as t b.

Answer 1

PLEASE REFER BELOW CODE

close all
clear all
clc

time_period = [0 1 1.8 2.1]; %given t values
initial_y = 0.5; %initial y values

[t,y] = ode45(@(t,y) ((t - exp(-t)) / (y + exp(y))) , time_period, initial_y); %ode45 using given DE
disp([t y])
plot(t,y,'-o'); %plot the expression
xlabel('t');
ylabel('y(t)');
title('y(t) versus t');

PLEASE REFER BELOW PLOT AND OUTPUT

0 0.5000
1.0000 0.4360
1.8000 0.8044
2.1000 0.9680

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y(t) versus t 0.9 0.8 0.7 0.6 0.5ф 0.4 L 0.5 2.5