Internal problem ID [7758]
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]
Solve \begin {gather*} \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=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 61
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)
\[ y \relax (x ) = 1-\frac {2 \sqrt {x}}{\sqrt {x -1}\, \sqrt {x +1}\, \left (c_{1}-\frac {2 \EllipticF \left (\sqrt {x +1}, \frac {\sqrt {2}}{2}\right ) \sqrt {-x}\, \sqrt {2}\, \sqrt {1-x}}{\sqrt {x -1}\, \sqrt {x}}\right )} \]
✓ 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} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};x^2\right )+c_1\right )} \\ y(x)\to 1 \\ \end{align*}