E.R.Kolchin has developed the differential Galois theory in 1950s. And it seems powerful a tool which can decide the solvability and the form of solutions to a given differential equation. My question is why differential Galois theory is not widely used in differential geometry. It is plausible that we can solve some problems of differential/integral […]

This question is an exact duplicate of: Correlation between the weak solutions of a differential equation and implied differential equations

I’ve come across statements in the past along the lines of “function $f(x)$ has no closed form integral”, which I assume means that there is no combination of the operations: addition/subtraction multiplication/division raising to powers and roots trigonometric functions exponential functions logarithmic functions which when differentiated gives the function $f(x)$. I’ve heard this said about […]

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