Internal problem ID [9953]
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. Form \(y y'-y=f(x)\). subsection 1.3.1-2. Solvable
equations and their solutions
Problem number: 47.
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-y-12 x -\frac {A}{x^{\frac {5}{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 119
dsolve(y(x)*diff(y(x),x)-y(x)=12*x+A*x^(-5/2),y(x), singsol=all)
\[ c_{1}+\frac {-168 x^{\frac {5}{2}} \sqrt {3}\, \left (4 x -y \relax (x )\right ) \hypergeom \left (\left [-\frac {1}{6}, \frac {1}{2}\right ], \left [\frac {3}{2}\right ], -\frac {3 x^{\frac {3}{2}} \left (4 x -y \relax (x )\right )^{2}}{4 A}\right )+3 \,2^{\frac {2}{3}} \left (\frac {48 x^{\frac {7}{2}}-24 y \relax (x ) x^{\frac {5}{2}}+3 x^{\frac {3}{2}} y \relax (x )^{2}+4 A}{A}\right )^{\frac {1}{6}} \left (48 x^{\frac {7}{2}}-24 y \relax (x ) x^{\frac {5}{2}}+3 x^{\frac {3}{2}} y \relax (x )^{2}+4 A \right ) \sqrt {3}}{\sqrt {-A \,x^{\frac {7}{2}}}} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==12*x+A*x^(-5/2),y[x],x,IncludeSingularSolutions -> True]
Not solved