Question

A second order differential equation can be graphed by using a double entry slopefield (lety,so '. Find the exact solution to the second-order differential equation y"+2y+5y 0 with initial conditions y(o)-2 and y (o--4, then graph with the double entry slopefield plot below. (5pts) RAD Examl 1.1 0.2 Exanill (04 0 2 -2 .2

Answer 1

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Matlab code for plotting the double entry slope field clear all close all Function for y(t) and y'(t) y-e(t) exp (-t)(2*cos (2*t)-sin(2*t)) z-e (t) exp(-t)4 cos (2*t)-3*sin (2*t)) All t values tt-linspace (0,10); %All y(t) and z(t) values for given t 22-2 (tt); figure(1) plot (tt, yy, r*') xlabel(') ylabel ( y(x) title(x vs. y(x) plot' grid orn figure (2) plot (tt, zz, 'r*) xlabel(x) ylabel'2 (x) ') title( 'x vs. z(x,-d (y(x))/dx plot' ) grid on figure (3) plot (tt,-2*yy-5*zz, r*) xlabel'x') ylabel( z(x) ') title(x vs. d(2 (x))/dx plot' grid on %%동号%%号号%%号号%%号号 End of Code 용융융욤욤응응용용융응용용응응용용융응

x vs. y(x) plot 1.5 05 -0.5 0 2345 678 910 vs. z(-dt()Vdx plot 3-2 0 2345 678910 2

x vs. d(z(x)Vdx plot 20 15 10 0 2345 678 910 Published with MATLAB R2018a

%%Matlab code for plotting the double entry slope field
clear all
close all

%Function for y(t) and y'(t)

y=@(t) exp(-t).*(2*cos(2*t)-sin(2*t));

z=@(t) exp(-t).*(-4*cos(2*t)-3*sin(2*t));
%All t values
tt=linspace(0,10);
%All y(t) and z(t) values for given t
yy=y(tt);
zz=z(tt);

figure(1)
plot(tt,yy,'r*')
xlabel('x')
ylabel('y(x)')
title('x vs. y(x) plot')
grid on

figure(2)
plot(tt,zz,'r*')
xlabel('x')
ylabel('z(x)')
title('x vs. z(x)=d(y(x))/dx plot')
grid on

figure(3)
plot(tt,-2*yy-5*zz,'r*')
xlabel('x')
ylabel('z(x)')
title('x vs. d(z(x))/dx plot')
grid on

%%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%%%