55.24.47 problem 47

Internal problem ID [13676]
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 : 47
Date solved : Thursday, October 02, 2025 at 12:23:35 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (24 x +11\right ) x^{{27}/{20}} y}{30}&=-\frac {a^{2} \left (x -1\right ) \left (9 x +1\right )}{60 x^{{17}/{10}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+1/30*a*(24*x+11)*x^(27/20)*y(x) = -1/60*a^2*(x-1)*(9*x+1)/x^(17/10); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/30*a*(24*x+11)*x^(27/20)*y[x]==-1/60*a^2*(x-1)*(9*x+1)*x^(-17/10); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a**2*(x - 1)*(9*x + 1)/(60*x**(17/10)) + a*x**(27/20)*(24*x + 11)*y(x)/30 + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out