Hi chadmcgrath,
I tried your differential equation with both MATLAB and Wolfram Alpha, but both failed to give a solution. However it could be easily seen that, y=0 is solution.
Hello, I'm a first time poster and a hobbyist who is trying to model a system,
I'm attempting to solve this ODE:
y' = cos(cx)sin(yx) where y is a function of x and c is a constant
I can't seem to get Mathematica (I just got a trial version) to do much with it and solving it on it's own is pretty hard.
Something that may be helpful: I have also considered that since, by the chain rule, if we make
g(x) = yx then
g'(x) = cos(cx). this is the little trick that might make this work
Using the product rule g'(x) =y'x + x'y = y'x+y = cos(cx) which can be rewritten as:
x*cos(cx)sin(yx)+y=cos(cx)
This is no longer an ODE. It's well, just an equation. But I'm nut sure how to simplify it into something i can graph, even though i've tried (using Mathematica) graphing it using the above and the complex exponential equivalent of the equation.
Help?
Hi chadmcgrath,
I tried your differential equation with both MATLAB and Wolfram Alpha, but both failed to give a solution. However it could be easily seen that, y=0 is solution.
Thanks for replying, I wasn't exactly clear on how making g[x] = yx is not allowed. In the original post, I say that y is a function of x (however it might not have been entirely apparent, and it might not help that I was mixing notations up now that I look back at it.). Maybe I'm the wrong track with that in any event but that has often worked for me in the past.
In that case I figured the derivative of sin(g[x]) is g'[x]Sin(g[x)). In this case yielding g'[x] = cos[x] as a possible solution.
This works(I think) for instance, in the case where the the left hand side is not equal to y'. Instead f'[x] = cos[x]Sin[yx] you can plug in y=sin[x]/x as a solution.
Is that all wrong?
The substitution leads to and hence
or
Still nasty. I've got Mathematica chewing on it right now. I'm guessing it's probably not going to work. Have you tried numerical solutions?
In what context did this DE show up?
I just wrote a very long reply but lost it. I apologize but I don't think the equation I gave you was smooth. So I'll have to work on the model before submitting something like this again.