61.22.21 problem 21

Internal problem ID [12267]
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 : 21
Date solved : Monday, March 31, 2025 at 04:57:50 AM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = 3/8*x+3/8*(a^2+x^2)^(1/2)-1/16*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]==3/8*x+3/8*Sqrt[x^2+a^2]-a^2/(16*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(a**2/(16*sqrt(a**2 + x**2)) - 3*x/8 - 3*sqrt(a**2 + x**2)/8 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out