61.24.36 problem 36

Internal problem ID [12449]
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 : 36
Date solved : Tuesday, January 28, 2025 at 07:59:23 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 167

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

\[ c_{1} -\frac {9 \,5^{{1}/{6}} 2^{{2}/{3}} \sqrt {\frac {x^{3} y+a x -a}{\left (x^{2} y+a \right ) x}}\, \left (x -\frac {3}{4}\right )}{5 x {\left (-\frac {a}{\left (x^{2} y+a \right ) x}\right )}^{{1}/{3}} \left (\frac {3 x^{3} y+3 a x -a}{\left (x^{2} y+a \right ) x}\right )^{{1}/{6}}}-729 \left (\int _{}^{\frac {\frac {9 x^{3} y}{5}+\frac {9 a x}{5}-\frac {27 a}{20}}{\left (x^{2} y+a \right ) x}}\frac {\textit {\_a} \sqrt {20 \textit {\_a} -9}}{\left (5 \textit {\_a} -9\right )^{{1}/{3}} \left (9+4 \textit {\_a} \right )^{{1}/{6}} \left (400 \textit {\_a}^{3}-1701 \textit {\_a} +729\right )}d \textit {\_a} \right ) = 0 \]

✗ Solution by Mathematica

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

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

Not solved