61.22.43 problem 43

Internal problem ID [12368]
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 : 43
Date solved : Tuesday, January 28, 2025 at 02:53:29 AM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=-\frac {3 x}{32}-\frac {3 \sqrt {a^{2}+x^{2}}}{32}+\frac {15 a^{2}}{64 \sqrt {a^{2}+x^{2}}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=-3/32*x-3/32*sqrt(x^2+a^2)+15*a^2/(64*sqrt(x^2+a^2)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]-y[x]==-3/32*x-3/32*Sqrt[x^2+a^2]+15*a^2/(64*Sqrt[x^2+a^2]),y[x],x,IncludeSingularSolutions -> True]
 

Not solved