Internal problem ID [10022]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.3-2. Equations of
the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime } y+\frac {a \left (7 x -12\right ) y}{10 x^{\frac {7}{5}}}+\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{\frac {9}{5}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 290
dsolve(y(x)*diff(y(x),x)+1/10*a*(7*x-12)*x^(-7/5)*y(x)=-1/10*a^2*(x-1)*(x-16)*x^(-9/5),y(x), singsol=all)
\[ c_{1}+\frac {\left (-\frac {x^{\frac {8}{5}} a +4 x^{\frac {3}{5}} a -5 x^{\frac {11}{10}} a +y \relax (x ) x}{10 x^{\frac {11}{10}} a}\right )^{\frac {3}{2}} \left (\frac {5 \left (x^{\frac {8}{5}} a +4 x^{\frac {3}{5}} a -5 x^{\frac {11}{10}} a +y \relax (x ) x \right ) \hypergeom \left (\left [-\frac {3}{2}\right ], \left [\right ], -\frac {x^{\frac {8}{5}} a +4 x^{\frac {3}{5}} a -5 x^{\frac {11}{10}} a +y \relax (x ) x}{10 x^{\frac {11}{10}} a}\right )}{8 x^{\frac {11}{10}} a}+\frac {25 \left (-x -2+3 \sqrt {x}\right ) \hypergeom \left (\left [-\frac {5}{2}\right ], \left [\right ], -\frac {x^{\frac {8}{5}} a +4 x^{\frac {3}{5}} a -5 x^{\frac {11}{10}} a +y \relax (x ) x}{10 x^{\frac {11}{10}} a}\right )}{4 \left (-x +2+\sqrt {x}\right )}\right )}{\frac {\left (\frac {3}{2}-\frac {5 \left (-x -2+3 \sqrt {x}\right )}{2 \left (-x +2+\sqrt {x}\right )}\right ) \hypergeom \left (\left [-4, 1\right ], \left [-\frac {1}{2}\right ], -\frac {x^{\frac {8}{5}} a +4 x^{\frac {3}{5}} a -5 x^{\frac {11}{10}} a +y \relax (x ) x}{10 x^{\frac {11}{10}} a}\right )}{2}+\frac {2 \left (x^{\frac {8}{5}} a +4 x^{\frac {3}{5}} a -5 x^{\frac {11}{10}} a +y \relax (x ) x \right ) \hypergeom \left (\left [-3, 2\right ], \left [\frac {1}{2}\right ], -\frac {x^{\frac {8}{5}} a +4 x^{\frac {3}{5}} a -5 x^{\frac {11}{10}} a +y \relax (x ) x}{10 x^{\frac {11}{10}} a}\right )}{5 x^{\frac {11}{10}} a}} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]+1/10*a*(7*x-12)*x^(-7/5)*y[x]==-1/10*a^2*(x-1)*(x-16)*x^(-9/5),y[x],x,IncludeSingularSolutions -> True]
Timed out