Internal problem ID [8515]
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]
\[ \boxed {3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y=3 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 190
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)
\[ y \left (x \right ) = \frac {80 c_{1} \sqrt {3}\, \pi \left (x^{2}-\frac {2}{5}\right ) \operatorname {LegendreP}\left (-\frac {1}{6}, -\frac {1}{3}, \frac {-x^{2}-1}{x^{2}-1}\right )+315 \Gamma \left (\frac {2}{3}\right ) \left (\frac {24 \left (x^{2}\right )^{\frac {1}{3}} \operatorname {LegendreP}\left (-\frac {1}{6}, \frac {1}{3}, \frac {-x^{2}-1}{x^{2}-1}\right ) \Gamma \left (\frac {2}{3}\right ) x^{\frac {4}{3}}}{35}+\left (x^{2}\right )^{\frac {1}{6}} \left (-x^{2}+1\right )^{\frac {5}{6}} \left (\left (x^{4}-x^{2}\right ) c_{1} \operatorname {hypergeom}\left (\left [\frac {11}{6}, \frac {13}{6}\right ], \left [\frac {7}{3}\right ], x^{2}\right )-\frac {6 \operatorname {hypergeom}\left (\left [\frac {3}{2}, \frac {11}{6}\right ], \left [\frac {5}{3}\right ], x^{2}\right ) \left (x^{\frac {4}{3}}-x^{\frac {10}{3}}\right )}{7}\right )\right )}{x^{\frac {1}{3}} \left (16 x^{\frac {2}{3}} \pi \sqrt {3}\, \operatorname {LegendreP}\left (-\frac {1}{6}, -\frac {1}{3}, \frac {-x^{2}-1}{x^{2}-1}\right ) c_{1} +72 \left (x^{2}\right )^{\frac {1}{3}} \operatorname {LegendreP}\left (-\frac {1}{6}, \frac {1}{3}, \frac {-x^{2}-1}{x^{2}-1}\right ) \Gamma \left (\frac {2}{3}\right )^{2}\right )} \]
✓ Solution by Mathematica
Time used: 4.513 (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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