Internal problem ID [8514]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 178.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y=-x^{2}+3} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 105
dsolve(2*x*(x^2-1)*diff(y(x),x) + 2*(x^2-1)*y(x)^2 - (3*x^2-5)*y(x) + x^2 - 3=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \sqrt {2}\, \operatorname {EllipticF}\left (\sqrt {x +1}, \frac {\sqrt {2}}{2}\right ) \sqrt {-x}\, \sqrt {1-x}\, \sqrt {x +1}-\sqrt {x -1}\, \sqrt {x}\, \sqrt {x +1}\, c_{1} +2 x}{\sqrt {x +1}\, \left (2 \operatorname {EllipticF}\left (\sqrt {x +1}, \frac {\sqrt {2}}{2}\right ) \sqrt {-x}\, \sqrt {2}\, \sqrt {1-x}-c_{1} \sqrt {x}\, \sqrt {x -1}\right )} \]
✓ Solution by Mathematica
Time used: 20.302 (sec). Leaf size: 54
DSolve[2*x*(x^2-1)*y'[x] + 2*(x^2-1)*y[x]^2 - (3*x^2-5)*y[x] + x^2 - 3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\frac {\sqrt {x}}{\sqrt {1-x^2} \left (2 \sqrt {x} \operatorname {Hypergeometric2F1}\left (\frac {1}{4},\frac {1}{2},\frac {5}{4},x^2\right )+c_1\right )} \\ y(x)\to 1 \\ \end{align*}