55.2.74 problem 74

Internal problem ID [13300]
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 : 74
Date solved : Wednesday, October 01, 2025 at 06:24:14 AM
CAS classification : [_rational, _Riccati]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 1218

ode:=x^2*(a*x^n-1)*(diff(y(x),x)+lambda*y(x)^2)+(p*x^n+q)*x*y(x)+r*x^n+s = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 3.074 (sec). Leaf size: 1882

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out