61.24.39 problem 39

Internal problem ID [12452]
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 : 39
Date solved : Tuesday, January 28, 2025 at 07:59:25 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 116

dsolve(y(x)*diff(y(x),x)+a*(x-2)*x^(-1)*y(x)=2*a^2*(x-1)*x^(-1),y(x), singsol=all)
 

\[ \frac {\sqrt {\frac {\left (1-x \right ) a -y}{a x +y}}\, {\mathrm e}^{\frac {a x +y}{2 a}} y+\left (a x +y\right ) \left (\int _{}^{\frac {a}{a x +y}}\frac {\sqrt {\textit {\_a} -1}\, {\mathrm e}^{\frac {1}{2 \textit {\_a}}}}{\sqrt {\textit {\_a}}}d \textit {\_a} +c_{1} \right ) x \sqrt {\frac {a}{a x +y}}}{\sqrt {\frac {a}{a x +y}}\, x \left (a x +y\right )} = 0 \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]+a*(x-2)*x^(-1)*y[x]==2*a^2*(x-1)*x^(-1),y[x],x,IncludeSingularSolutions -> True]
 

Not solved