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Results tagged with differential-galois-theory
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user 11260
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Why the Riccati equation $\frac{\mathrm{d} y}{\mathrm{d} x} =ax^{m}+by^{2}$ has an elementar...
For $m\neq -2$ the solution contains the Bessel function $J_{\nu}\left(\frac{2 \sqrt{a b}\, x^{1+m/2}}{m+2}\right)$ with index $\nu=\pm(m+2)^{-1}$, $\nu=-1\pm(m+2)^{-1}$, and $\nu=1\pm(m+2)^{-1}$. The …
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