55.2.17 problem 17

Internal problem ID [13243]
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 : 17
Date solved : Wednesday, October 01, 2025 at 04:02:25 AM
CAS classification : [_rational, _Riccati]

\begin{align*} \left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 1048

ode:=(c__2*x^2+b__2*x+a__2)*(diff(y(x),x)+lambda*y(x)^2)+a__0 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 4.316 (sec). Leaf size: 1045

ode=(c2*x^2+b2*x+a2)*(D[y[x],x]+\[Lambda]*y[x]^2)+a0==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__0 = symbols("a__0") 
a__2 = symbols("a__2") 
b__2 = symbols("b__2") 
c__2 = symbols("c__2") 
lambda_ = symbols("lambda_") 
y = Function("y") 
ode = Eq(a__0 + (lambda_*y(x)**2 + Derivative(y(x), x))*(a__2 + b__2*x + c__2*x**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out