Analyzing Nonlinear Differential Equations: Do Analytic Solutions Exist?

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can non linear differential equations have analytic solutions?
In fact, can you please explain why is it so?
Thanks in advance! :)
 
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I hope this to be answered! :)
 

Thread 'Visual Representation of Separation of Varables'

Are there any good visualization tutorials, written or video, that show graphically how separation of variables works? I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another. However I am trying to visualize in my mind how this process looks graphically - for example plotting t on one axis and x on the other for f(x,t). I have seen other good visual representations of...
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