Help with using the contour function with differential equations

[adityagaddam]

Hi,

I am trying to draw several solutions to a different equation. I have the following in MATLAB

>>eqn = 'Dy = (-exp)/((t*exp - sin))';

>>dsolve(eqn, 't')
Warning: Explicit solution could not be found; implicit solution returned.
> In dsolve at 312
ans =

t+exp(-y)*cos-exp(-y)*C1 = 0

>>f = @(t, y) (-t)/(exp(-y)*cos-exp(-y)); (solved for C1)
>>[T, Y] = meshgrid(-1:0.1:4, 0:0.1:3); (ranges were given)
>>contour(T, Y, f(T, Y), 30, 'k')

When I do the last contour instruction however, I get an error saying:
"??? Error using ==> mtimes
Inner matrix dimensions must agree."

I tried switching around ranges but I don't see what's wrong with the commands I have.

Any help or ideas is appreciated.

Thanks,
Aditya

 

[VisiGoth]

Without having trying this I have a quick observation based on the code.

f = @(t, y) (-t)/(exp(-y)*cos-exp(-y)); (solved for C1)

looks like you are attempting matrix / and * instead of maybe point by point. Try ./ and .* instead.

 

[adityagaddam]

Well, it's sort of better now. It does SOMETHING for contour(T, Y, f(T, Y), 30, 'k'), but then errors out saying :

Warning: Divide by zero.
> In @(t, y) (-t)./(exp(-y).*cos-exp(-y))
??? Error using ==> contourc
Contour levels must be finite.

Warning: Error occurred while evaluating listener callback.
> In contour at 66

I am guessing it doesn't like the dividing by zero and then goes downhill from there?

Any ideas?

Thanks,
Aditya

 

[VisiGoth]

Try a hack. It may get you close, or put a switch in you function to test for divide by zer and supply the correct answer instead.

The eps hack:
f = @(t, y) (-t)/(eps+exp(-y)*cos-exp(-y));

 

[adityagaddam]

The eps hack worked, but all the curves are squished to the bottom of the plot, would the switch in the function work better? ifso, how would you do this switch?

Thanks,
Aditya

 

[adityagaddam]

I am sorry, I was doing something else wrong, but I really appreciate you quick help.

Thanks a lot,
Aditya

 

[VisiGoth]

OK. Good. Thanks for the kind words.
See the sinc.m file for an example. MATLAB does a test for the same reason and avoids the eps hack.