How do I add a legend to my plot?

%Define the variables using syms - syms creates symbolic variables

syms y(t) y0

%define the ordinary differential equation

ode = diff(y,t) == cos(t^2);

%solve the differential equation using dsolve

ysol = dsolve(ode,y(0)==y0);

%Create a figure called Task 1

figure ('Name','Task 1')

%Pick 3 different initial conditions for which the solution exists
%Conditions are the y values (y values are 1, 1.5, and 3 at varying t
%values. See the t values below.

conds = [1 1.5 3]'; %some values of y0

f = matlabFunction(subs(ysol,y0,conds));
t = linspace(0,50);
y = f(t);

%plotting the 3 equations

plot(t,y,'linewidth',2)
title('Symbolic Solutions')
xlabel('t')
ylabel('y(t)')
grid on

Answer 1

[Star Strider]

To add the legend, either use sprintfc (undocumented although quite useful):

lgndc = sprintfc('IC = %.1f',conds);
legend(lgndc, 'Location','E')

or compose:

lgndc = compose('IC = %.1f',conds);
legend(lgndc, 'Location','E')

both produce the same result.

Put these lines after your ‘grid on’ call.

[Vincenzo Dragone]

For some reason this isn't working in my code...I replaced the IC with my initial condition y(0)...

[Star Strider]

What does ‘not working’ mean?

I copied your code exactly and added only those two lines. (I am running R2019a.)

%Define the variables using syms - syms creates symbolic variables
syms y(t) y0
%define the ordinary differential equation
ode = diff(y,t) == cos(t^2);
%solve the differential equation using dsolve
ysol = dsolve(ode,y(0)==y0);
%Create a figure called Task 1
figure ('Name','Task 1')
%Pick 3 different initial conditions for which the solution exists
%Conditions are the y values (y values are 1, 1.5, and 3 at varying t
%values. See the t values below.
conds = [1 1.5 3]'; %some values of y0
f = matlabFunction(subs(ysol,y0,conds));
t = linspace(0,50);
y = f(t);
%plotting the 3 equations
plot(t,y,'linewidth',2)
title('Symbolic Solutions')
xlabel('t')
ylabel('y(t)')
grid on
lgndc = sprintfc('IC = %.1f',conds);
legend(lgndc, 'Location','E')

[Vincenzo Dragone]

I am running R2018b which is why I think it's a problem.

It keeps giving me the following error.

Unable to use a value of type 'cell' as an index.

Error in Untitled3 (line 23)

legend(lgndc, 'Location','E')

[Star Strider]

Running R2018b is not the problem.

In your Command Window, type:

which('legend','-all')

and post all the results in a Comment here.

The only results should be something like:

C:\Program Files\MATLAB\R2019a\toolbox\matlab\scribe\legend.p
C:\Program Files\MATLAB\R2019a\toolbox\matlab\scribe\legend.m  % Shadowed

I suspect you will have more outputs than that, and the extra outputs should direct you to finding the problem.

[Vincenzo Dragone]

I downloaded the R2019a version to my computer and got it to work. Thank you!

[Star Strider]

My pleasure.

If my Answer helped you solve your problem, please Accept it!

[Vincenzo Dragone]

I'm trying to accept, but I don't see where the button is???

[Star Strider]

It should be something like this:

Thank you!

[Rena Berman]

(Answers dev) Vincenzo, I have accepted the answer for you. Were you logged in when you couldn't see the button? What commands do you have available to you under Star Strider's picture (which is just to the left of his answer?) For example:

If you are logged in, you should be able to see an accept/unaccept option right under the vote/unvote command. This is in addition to the "Accept this answer" button that Star Strider mentions above.

[Vincenzo Dragone]

Hi Rena,

Yes, I am logged into my account. But the accept/unaccept option was not popping up. I saw it last night, forgot to hit it, but then this morning I couldn't find it.

The commands under Star Strider's picture are Vote, Flag, and Link. That's all.

[Rena Berman]

(Answers dev) Thanks for the quick reply! I'll look in to it.

[Star Strider]

Thank you both!

[Vincenzo Dragone]

Star Strider,

Would you be able to help me with another question?

Using Euler's Method, I need to approximate the solution to the IVP over some t range which I get to choose and then plot it.

My initial condition is y(0)=1 like in Task 1 code.

Here is all the code I have so far.

%% Task 1: Solve the ODE using the Symbolic Math Package and dsolve()

%Define the variables using syms - syms creates symbolic variables

syms y(t) y0 y1 h ode y2

%define the ordinary differential equation

ode = diff(y,t) == cos(t^2);

%solve the differential equation using dsolve

ysol = dsolve(ode,y(0)==y0);

%Create a figure called Task 1

figure ('Name','Task 1')

%Pick 3 different initial conditions for which the solution exists

%Conditions are the y values (y values are 1, 1.5, and 3 at varying t

%values. See the t values below.

conds = [1 1.5 2]'; %some values of y0

f = matlabFunction(subs(ysol,y0,conds));

t = linspace(0,5);

y = f(t);

%plotting the 3 equations

plot(t,y,'linewidth',2)

title('Symbolic Solutions')

xlabel('t')

ylabel('y(t)')

grid on

lgndc = sprintfc('IC = %.1f',conds);

legend(lgndc, 'Location','E')

%% Task 2: Euler's Method

%Pick a single initial condition from Task 1

%The initial condition we will use is y(0)=1

%Use Euler's method to approximate the solution to this IVP over some t

%range which you choose

%Create a figure called Task 2

figure ('Name','Task 2')

%The range of t is from 0 to 1

%We are using the initial condition that y(0)=1, but we want to know y(t)

%when t=1

%In other words we want to find y(1)

y = y0;

yout = y;

t0 = 0;

h = 0.5;

tfinal = 50;

for t= t0 : h : tfinal-h

y = y + h*ode;

yout = [yout;y]

end

[Star Strider]

Jim Riggs already appears to have answered that to your satisfaction: How do you use Euler's Method to approximate the solution?

I doubt that I could improve on his Answer:.