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Me, too.
At first, I thought this is just an ordinary diff equation, just like:
y' = y + x
But it's really a big problem when y' is in the denominator like this
1/y' = 1/y + 1/x
This diff equation does not have the form like any that I've learnt before. Maybe it's just because I don't know how to use sub-variable.
However, I think there are some diff equations having root that can not be expressed by normal functions that we've known.
Does anyone here know how to prove the root of this diff equation can not be expressed by normal functions like sin, cos, exponential, polynomical,...?
I am also very much interested in solution of this differntial equation.
I also tried hard enough but no luck. It seems to be a nonlinear differntial
eq.
Differential equation whose solution satifies the existence and uniqueness can be solved by using Lie-algebra. The problem then is to find the suitable infinitesimal transformation which can be admitted by the equation itself. More information in the classic book "Symmetries and Differential Equations" G.W.Bluman, S.Kumei, Springer-Verlag 1989. A powerful package for Mathematica developed by Gerd Baumann is availabe in his book "Symmetry Analysis of Differential Equation with Mathematica".
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