55.25.10 problem 10

Internal problem ID [13719]
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 1.3.4-2.
Problem number : 10
Date solved : Thursday, October 02, 2025 at 04:04:52 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (\left (3 a x +\lambda s \right ) y+\left (3 s +4 \lambda \right ) x \right ) y^{\prime }&=2 a y^{2}+6 \lambda +2 s +2 x \end{align*}

✗ Maple

ode:=((3*a*x+lambda*s)*y(x)+(3*s+4*lambda)*x)*diff(y(x),x) = 2*a*y(x)^2+6*lambda+2*s+2*x; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=((3*a*x+\[Lambda]*s)*y[x]+(4*\[Lambda]+3*s)*x)*D[y[x],x]==2*a*y[x]^2+2*(3*\[Lambda]+s)+2*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
lambda_ = symbols("lambda_") 
s = symbols("s") 
y = Function("y") 
ode = Eq(-2*a*y(x)**2 - 6*lambda_ - 2*s - 2*x + (x*(4*lambda_ + 3*s) + (3*a*x + lambda_*s)*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out