I'm trying to plot this contour graph, but it just does not work?
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I tried to solve this differential equation: e^y+(t*e^y - sin(y))*(dy/dt)=0
using the symbolic solver dsolve, I inputed this and got: RootOf(_Z-log(-(cos(_Z)-C1)/t)) % where C1 is just some arbitrary constant and _Z is the placeholder of Y
so the solution I am trying to graph is this: y-log(-(cos(y))/t)
I first tried to do it by using anonymous equation:
fun=@(t,y) (y-log(-cos(y))./t); [T Y]= meshgrid(-1:0.1:4, 0:0.1:3); contour(T,Y, fun(T,Y),30,'k')
It just gave me a empty graph, so then I tried doing it without anonymous function: [T Y]= meshgrid(-1:0.1:4, 0:0.1:3); Z=(Y-log(-cos(Y))./T); contour(Z,30)
I still get an empty graph.
I do not know if it has to do with the axis or whatever, but I do notice that some of the numerical values are imaginary numbers. Could that have something to do with it? Can someone please help me out?
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Walter Roberson
2011-7-25
I am not certain at the moment that your approach is correct.
The Maple expression RootOf(Z-log(-(cos(_Z)-C1)/t)) does not mean that _Z is an arbitrary number: rather _Z stands in place there the entire set of numbers, set Z, such that when a member of set Z is substitute in place of _Z in the expression, that the expression enclosed in RootOf() will evaluate to 0. The _Z are, in other words, the root of the equation enclosed in RootOf(), and the _value of the RootOf() expression is logically that set of roots
Varying C1 and t in the RootOf(), I can see that the graph of the roots can look "mostly linear" for some ranges of values, but that if you probe more carefully there are areas it is non-linear, such as along the line C1=t .
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