55.2.71 problem 71

Internal problem ID [13297]
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 : 71
Date solved : Wednesday, October 01, 2025 at 06:16:26 AM
CAS classification : [_rational, _Riccati]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out