Internal problem ID [7759]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 179.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 145
dsolve(3*x*(x^2-1)*diff(y(x),x) + x*y(x)^2 - (x^2+1)*y(x) - 3*x=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (35 x^{4} c_{1}-35 c_{1} x^{2}\right ) \hypergeom \left (\left [\frac {11}{6}, \frac {13}{6}\right ], \left [\frac {7}{3}\right ], x^{2}\right )}{8 x^{\frac {1}{3}} \left (\hypergeom \left (\left [\frac {5}{6}, \frac {7}{6}\right ], \left [\frac {4}{3}\right ], x^{2}\right ) x^{\frac {2}{3}} c_{1}+\hypergeom \left (\left [\frac {1}{2}, \frac {5}{6}\right ], \left [\frac {2}{3}\right ], x^{2}\right )\right )}+\frac {\left (40 c_{1} x^{2}-16 c_{1}\right ) \hypergeom \left (\left [\frac {5}{6}, \frac {7}{6}\right ], \left [\frac {4}{3}\right ], x^{2}\right )+\left (30 x^{\frac {10}{3}}-30 x^{\frac {4}{3}}\right ) \hypergeom \left (\left [\frac {3}{2}, \frac {11}{6}\right ], \left [\frac {5}{3}\right ], x^{2}\right )+24 \hypergeom \left (\left [\frac {1}{2}, \frac {5}{6}\right ], \left [\frac {2}{3}\right ], x^{2}\right ) x^{\frac {4}{3}}}{8 x^{\frac {1}{3}} \left (\hypergeom \left (\left [\frac {5}{6}, \frac {7}{6}\right ], \left [\frac {4}{3}\right ], x^{2}\right ) x^{\frac {2}{3}} c_{1}+\hypergeom \left (\left [\frac {1}{2}, \frac {5}{6}\right ], \left [\frac {2}{3}\right ], x^{2}\right )\right )} \]
✓ Solution by Mathematica
Time used: 3.294 (sec). Leaf size: 3149
DSolve[3*x*(x^2-1)*y'[x] + x*y[x]^2 - (x^2+1)*y[x] - 3*x==0,y[x],x,IncludeSingularSolutions -> True]
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