I'm trying to use dsolve to solve this differential equation, but it does not work

I'm trying to solve this differential equation using dsolve in matlab, so this is what Im trying to run:

eqn = 'Dy=-exp(y)/(t*exp(y)-sin(y))';
dsolve(eqn,'t')

I know that there is no explicit solution to it, but I was taught that matlab should return a implicit solution. However it doesn't. I've tried it on different versions of matlab, but still no luck. Can someone please help me out?

**this is the error it returns: 
??? Error using ==> mupadmex
Error in MuPAD command: wrong 2nd argument [normal]

Error in ==> sym.sym>sym.mupadmexnout at 2003
out = mupadmex(fcn,args{:});

Error in ==> dsolve>mupadDsolve at 190
[var_list,R] = mupadmexnout('mllib::dsolve',sys,x,ignor…

Error in ==> dsolve at 97
[R,vars] = mupadDsolve(ignoreConstraints,varargin{1…

[Robin]

this was the original question asked on the assignment btw:

consider the differential equation e^y+(t*e^y - sin(y))*(dy/dt)=0

using dsolve, observe that the solution is given in the form f(t,y)=C

(however I cannot get matlab to give me a solution at all)

Answer 1

[Walter Roberson]

Do you want to solve for y(t) rather than for t ? dsolve() really isn't suitable for solving for variables.

[Robin]

yes I am trying to solve it for y(t), where t is the independent variable. I know that dsolve is not the best method for this type of equation, but I still need to get a implicit solution out of this.

[Walter Roberson]

I have no difficulty in Maple:

> dsolve(diff(y(t),t)=-exp(y(t))/(t*exp(y(t))-sin(y(t))),y(t));

t+exp(-y(t))*cos(y(t))-exp(-y(t))*_C1 = 0

Try

evalin(symengine,'dsolve(diff(y(t),t)=-exp(y(t))/(t*exp(y(t))-sin(y(t))),y(t))')

[Robin]

this is what I ran:

evalin(symengine,'dsolve(diff(y(t),t)=-exp(y(t))/(t*exp(y(t))-sin(y(t))),y(t))')

and this was the output

ans =

dsolve(diff(y(t), t) = exp(y(t))/(sin(y(t)) - t*exp(y(t))), y(t))

....so it didn't really solve the differential equation at all :(

[Robin]

...thank you for trying to help me out, I've added some details to my original questions ^

[Walter Roberson]

This might help:

http://www.mathworks.com/matlabcentral/answers/5108-mupad-differential-equation-solver

The reference page is

http://www.mathworks.com/help/toolbox/mupad/stdlib/ode.html

[Walter Roberson]

You might get a different answer if you try to solve directly instead of in your reordered version. In Maple,

> dsolve(exp(y(t))+(t*exp(y(t))-sin(y(t))*diff(y(t),t)));

t+1/2*t^2+1/2*exp(-y(t))*cos(y(t))+1/2*exp(-y(t))*sin(y(t))+_C1 = 0

I do not myself see any difference between what you requested and the direct form, but Maple gives different answers for the two forms, and the larger form is a fit for the assignment question.

[Robin]

I tried it on a an older version of Matlab (2008) and it somehow worked, it gave me the RootOf(_Z-log(-(cos(_Z)-C1)/t)); where _z is the y. C1 is just some arbitrary constant...

[Walter Roberson]

That must have been a Maple based symbolic toolbox. We can tell that by the fact that it used _Z as the dummy variable for the RootOf(), which is Maple style; MuPad generates an arbitrary variable name that does not start with '_', and MuPad includes that dummy variable name as the second parameter of the RootOf().

It seems, then, that what has been tried works on the Maple symbolic engine, but not on MuPad. Unfortunately I do not have MuPad to test with.

Answer 2

[Rohith]

For me, I found that you need to add an option setting Implicit to true.

syms y(t)
eqn = exp(y) + (t*exp(y) - sin(y))*diff(y,t) == 0;
dsolve(eqn, 'Implicit', true)

ans = 

The output was:

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

[Abeda]

It doesn't run on online compiler of matlab octave

[Abeda]

Is there any other solution?

[Abeda]

Is it run on matlab 2021a version? Because, dsolve normally doesn't run on my laptop. Please, help me.