Problem 10 \"Differential Equations with Matlab\" Second Edition by Hunt Need pa

Question

Problem 10 "Differential Equations with Matlab" Second Edition by Hunt

Need parts B and C

iiis lunction is an antiderivative f sin t/t by differentiatingit (c) Evaluate limSi( functioll Si(t). Plot Si(t) and discuss the features of the graph. same with the solution to the initial value problem. solve the initial l the initial value problem using ode45, and plot the computed so- (e) Now Compare your plot to the one obtained in part (d). You will find that lutio. A B cannot evaluate sint/t at t 0, even though the singularity is re- le One way to get around this is to give the initial condition y-1 at a ft extremely close to, but not equal to, zero. Since we are only finding roximate solution with ode45 anyhow, there shouldn't be much harm as the amount by which we move the initial condition is small mova done as long with the error we expect from the numerical procedure. com the stability of the differential equation. Illustrate your conclusions by graphing solutions with different initial values on the interval |-10, 10) Note: In this problem some of your plots may take a long time to generate. Golve the following initial value problems numerically, then plot the solutions. Based on your plots, predict what happens to each solution as t increases. In particular, if there is a limiting value for y, either finite or infinite, find it. If it is unclear from the plot you've made, try replotting on a larger interval. Another possibility is that the solution blows up in finite time. If so, estimate the time when the solution blows up. Try to use the qualitative methods of Chapter 7 to confirm your answers. (a) y-e3(0)1. (b) y, e-2t + y2, y(0)-1. (c) y cost - y3, y(0) 0 (d) y' (sin t)y-y2, y(0) 2. -3t 1 + y Solve the following initial value problems numerically, then plot the solutions. Based on your plots, predict what happens to each solution as t increases. See Problem 10 for additional instructions. (b) y' (t3 -y3) cos y, y(0)1. t2+3

Explanation / Answer

general code differential equations hasbeen given below

MATLAB CODE FOR 10.b:

clc
clear

syms y(t)
Dy = diff(y);

ode = diff(y,t,1) == ((y^2)+exp(-2*t));

cond1 = y(0) == 1;
conds = [cond1];
ySol(t) = dsolve(ode,conds);
ySol = simplify(ySol);

pretty(ySol)

MATLAB CODE FOR 10.c:

clc
clear

syms y(t)
Dy = diff(y);

ode = diff(y,t,1)-(y^3) == (cos(t));

cond1 = y(0) == 0;
conds = [cond1];
ySol(t) = dsolve(ode,conds);
ySol = simplify(ySol);
pretty(ySol)

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