61.2.64 problem 64

Internal problem ID [11991]
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 : 64
Date solved : Sunday, March 30, 2025 at 10:04:26 PM
CAS classification : [_rational, _Riccati]

\begin{align*} \left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b_{1} x +a_{1} \right ) y+a_{0}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 2072

ode:=(c__2*x^2+b__2*x+a__2)*(diff(y(x),x)+lambda*y(x)^2)+(b__1*x+a__1)*y(x)+a__0 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 9.259 (sec). Leaf size: 1986

ode=(c2*x^2+b2*x+a2)*(D[y[x],x]+\[Lambda]*y[x]^2)+(b1*x+a1)*y[x]+a0==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
a__0 = symbols("a__0") 
a__1 = symbols("a__1") 
a__2 = symbols("a__2") 
b__1 = symbols("b__1") 
b__2 = symbols("b__2") 
c__2 = symbols("c__2") 
lambda_ = symbols("lambda_") 
y = Function("y") 
ode = Eq(a__0 + (a__1 + b__1*x)*y(x) + (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