61.22.47 problem 47

Internal problem ID [12372]
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 1.3.1-2. Solvable equations and their solutions
Problem number : 47
Date solved : Tuesday, January 28, 2025 at 07:57:18 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=12 x +\frac {A}{x^{{5}/{2}}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 110

dsolve(y(x)*diff(y(x),x)-y(x)=12*x+A*x^(-5/2),y(x), singsol=all)
 

\[ c_{1} +\frac {12 \sqrt {3}\, \left (2^{{2}/{3}} \left (\frac {3 y^{2} x^{{3}/{2}}}{4}-6 y x^{{5}/{2}}+A +12 x^{{7}/{2}}\right ) \left (\frac {48 x^{{7}/{2}}-24 y x^{{5}/{2}}+3 y^{2} x^{{3}/{2}}+4 A}{A}\right )^{{1}/{6}}-56 x^{{5}/{2}} \operatorname {hypergeom}\left (\left [-\frac {1}{6}, \frac {1}{2}\right ], \left [\frac {3}{2}\right ], -\frac {3 x^{{3}/{2}} \left (y-4 x \right )^{2}}{4 A}\right ) \left (x -\frac {y}{4}\right )\right )}{\sqrt {-A \,x^{{7}/{2}}}} = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]*D[y[x],x]-y[x]==12*x+A*x^(-5/2),y[x],x,IncludeSingularSolutions -> True]
 

Not solved