61.24.51 problem 51

Internal problem ID [12464]
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 : 51
Date solved : Tuesday, January 28, 2025 at 07:59:33 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 190

dsolve(y(x)*diff(y(x),x)-1/5*a*(x+4)*x^(-8/5)*y(x)=1/5*a^2*(x-1)*(3*x+7)*x^(-11/5),y(x), singsol=all)
 

\[ \frac {\frac {360 \,2^{{1}/{3}} \sqrt {-\frac {\left (x -1\right ) a +y x^{{3}/{5}}}{x^{{3}/{5}} \left (y+a \,x^{{2}/{5}}\right )}}\, \sqrt {17}\, 91^{{5}/{6}} \left (x -\frac {21}{4}\right ) \left (\frac {\left (3 x +7\right ) a +3 y x^{{3}/{5}}}{x^{{3}/{5}} \left (y+a \,x^{{2}/{5}}\right )}\right )^{{7}/{6}}}{4444531}[phone] \left (\frac {a}{x^{{3}/{5}} \left (y+a \,x^{{2}/{5}}\right )}\right )^{{5}/{3}} x \left (\int _{}^{-\frac {315 \left (4 y x^{{3}/{5}}+4 a x -21 a \right )}{884 \left (y x^{{3}/{5}}+a x \right )}}\frac {\left (68 \textit {\_a} +315\right )^{{1}/{6}} \sqrt {52 \textit {\_a} -315}\, \textit {\_a}}{\left (11492 \textit {\_a}^{2}-53235 \textit {\_a} -99225\right ) \left (221 \textit {\_a} +315\right )^{{5}/{3}}}d \textit {\_a} +\frac {c_{1}}{31255875}\right )}{\left (\frac {a}{x^{{3}/{5}} \left (y+a \,x^{{2}/{5}}\right )}\right )^{{5}/{3}} x} = 0 \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]-1/5*a*(x+4)*x^(-8/5)*y[x]==1/5*a^2*(x-1)*(3*x+7)*x^(-11/5),y[x],x,IncludeSingularSolutions -> True]
 

Timed out