Question

USING MATLAB

Please post code

1. Solve the 2nd order differential equation ?+89 +15y-sin(t), y(0)-1,?(0)-2 symbolically and numerically, and plot both results together over the time interval 0,10 sec. Provide appropriate labels on both axes, a title, and a legend that denotes each solution. Check your symbolic answer by using the Matlab DIFF function to compute the appropriate derivatives and then substituting them into the differential equation.

Answer 1

PLEASE REFER BELOW CODE

close all
clear all
clc

syms y(t)
%Solving DE symbolically

%given equation
eqn = diff(y,t,2) + 8 * diff(y,t,1) + 15 * y == sin(t);
Dy = diff(y,t);
cond = [y(0) == 1,Dy(0)==2]; %initial condition
ySol(t) = dsolve(eqn,cond);

t = 0:0.1:10;
hold on
plot(t,ySol(t))

%Solving numeriaclly
tspan = [0 10];
y0 = [1 2]; %initial condition
[t,y] = ode45(@dydt,tspan,y0);
plot(t,y(:,1))
hold off
title('Solution of DE');
xlabel('t');
ylabel('y(t)');
legend('Symbolically','Numerically')

function doty = dydt(t,y)
doty = [y(2); -8 * y(2)-15 * y(1)+sin(t)];
end

PLEASE REFER BELOW OUTPUT

Solution of DE 1.2 r Symbolically Numerically 0.8 0.6 0.4 0.2 -0.2 0 1 234 5 6 78 9 10