55.24.78 problem 78

Internal problem ID [13707]
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 : 78
Date solved : Thursday, October 02, 2025 at 03:20:02 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }&=\left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right ) \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x) = (2*ln(x)^2+2*ln(x)+a)*y(x)+x*(-ln(x)^4-a*ln(x)^2+b); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]==(2*(Log[x])^2+2*Log[x]+a)*y[x]+x*(- (Log[x])^4-a*(Log[x])^2+b); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(-x*(-a*log(x)**2 + b - log(x)**4) - (a + 2*log(x)**2 + 2*log(x))*y(x) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out