55.22.43 problem 43

Internal problem ID [13584]
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 : Wednesday, October 01, 2025 at 06:09:59 PM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-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*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = -3/32*x-3/32*(a^2+x^2)^(1/2)+15/64*a^2/(a^2+x^2)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=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]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-15*a**2/(64*sqrt(a**2 + x**2)) + 3*x/32 + 3*sqrt(a**2 + x**2)/32 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out