In my textbooks every now and again it says "these equations can't be solved analytically" or just "this can't be solved". For example my current book claims:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{dx}{dt}=-kBe^{kz}\sin(kx-\omega t) [/tex], and

[tex] \frac{dz}{dt}=kBe^{kz}\cos(kx-\omega t) [/tex],

can't be solved analytically.

How do they know it can't be solved? I hope its the case that someone has proved it can't be solved, however I have never seen these proofs (I don't think). Is there an area of maths that that I can have a look at to understand more about how they make these statements? Or can anyone point me to some simple proof showing certain types of PDE's or polynomials or the above or something not too complicated that can't be solved?

Thanks for any help.

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# Cannot be solved analytically

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