55.2.19 problem 19

Internal problem ID [13245]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.2. Riccati Equation. 1.2.2. Equations Containing Power Functions
Problem number : 19
Date solved : Wednesday, October 01, 2025 at 04:05:23 AM
CAS classification : [_rational, _Riccati]

\begin{align*} a \,x^{2} \left (x -1\right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 1077

ode:=a*x^2*(x-1)^2*(diff(y(x),x)+lambda*y(x)^2)+b*x^2+c*x+s = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

ode=a*x^2*(x-1)^2*(D[y[x],x]+\[Lambda]*y[x]^2)+b*x^2+c*x+s==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
lambda_ = symbols("lambda_") 
s = symbols("s") 
y = Function("y") 
ode = Eq(a*x**2*(x - 1)**2*(lambda_*y(x)**2 + Derivative(y(x), x)) + b*x**2 + c*x + s,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out