Question

4. MATLAB can solve second order equations numerically, but it needs to convert it to a sys- tem first. We haven't covered systems yet, but we can make use of them (entirely in MAT- LAB) to solve this problem. The help page https://www.mathworks.com/help/symbolic/ solve-differential-equation-numerically-1.html shows how to do this. Follow those steps to get the solution to day +9y = cos(3) dt2 y(0) = 0 v(0) = 0 Plot this and your solution from the previous part on the same axes. Do they match? 5. MATLAB can also solve second order equations symbolically using the Symbolic packages. The help page https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation. html#f1-11214 shows examples of how this works. Code this up for the same equation and see if you get the same answer. If you don't (and you probably won't), try simplifying the answer after you get it to see if it matches then. Note: You'll need to define the symbolic function y(t) here in order to use the same notation we did above. Also, you need to make a new variable Dy diff(y), otherwise the function notation won't work properly.

QUESTION 5 please.

Answer 1

`Hey,

Note: If you have any queries related to the answer please do comment. I would be very happy to resolve all your queries.

clc

clear all

close all

format short

syms y(t) Dy(t)

eq=diff(y,2)+9*y==cos(3*t);

Dy(t)=diff(y);

cond=[y(0)==0 Dy(0)==0];

y(t)=dsolve(eq,cond)

ezplot(y,[0,10]);

cos(9 t972 -...+ sin(3 t) (1/6 + sin(6 AM 1.5 1 х 0.5 Comment % Indent 5 EDIT Documents ► MATL Editor - /Use saveee.m 1 - clc 2 - clear 3 - close 4 - format syms y 6 eq=dif 7 Dy(t)= 8 cond=[ 9 y(t)=d 10 ezplot 11 Works Name o con Dy eq Ut Oy 0 M -0.5 - -1.5 0 1 2 3 4 6 7 8 9 10 5 t lol Command Window New to MATLAB? See resources for Getting Started. х y(t) = cos (9*t)/72 - cos (3*t)/72 + sin(3*t)*(t/6 + sin(6*t)/36)

Kindly revert for any queries

Thanks.