61.24.53 problem 53

Internal problem ID [12466]
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.
Problem number : 53
Date solved : Tuesday, January 28, 2025 at 07:59:45 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 156

dsolve(y(x)*diff(y(x),x)+1/5*a*(x-6)*x^(-7/5)*y(x)=2/5*a^2*(x-1)*(x+4)*x^(-9/5),y(x), singsol=all)
 

\[ c_{1} -\frac {80 \left (a y x^{{2}/{5}}+\frac {x^{{4}/{5}} y^{2}}{8}+\frac {\left (y x^{{7}/{5}}-2 a \left (x +24\right ) \left (x -1\right )\right ) a}{24}\right ) \sqrt {\frac {-y x^{{2}/{5}}-a x +a}{x^{{2}/{5}} \left (y+x^{{3}/{5}} a \right )}}\, \sqrt {3}\, \left (a y x^{{2}/{5}}+\frac {x^{{4}/{5}} y^{2}}{8}+\frac {a \left (y x^{{7}/{5}}+\frac {a \left (x +4\right )^{2}}{2}\right )}{4}\right )}{9 \left (\frac {a}{x^{{2}/{5}} \left (y+x^{{3}/{5}} a \right )}\right )^{{5}/{2}} \left (a \left (x +4\right )+y x^{{2}/{5}}\right )^{2} x \left (y x^{{2}/{5}}+a x \right )^{2}} = 0 \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]+1/5*a*(x-6)*x^(-7/5)*y[x]==2/5*a^2*(x-1)*(x+4)*x^(-9/5),y[x],x,IncludeSingularSolutions -> True]
 

Timed out