61.2.67 problem 67

Internal problem ID [11994]
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 : 67
Date solved : Sunday, March 30, 2025 at 10:06:37 PM
CAS classification : [_rational, _Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 613

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

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

✓ Mathematica. Time used: 1.592 (sec). Leaf size: 862

ode=x*(x^2+a)*(D[y[x],x]+\[Lambda]*y[x]^2)+(b*x^2+c)*y[x]+s*x==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") 
b = symbols("b") 
c = symbols("c") 
lambda_ = symbols("lambda_") 
s = symbols("s") 
y = Function("y") 
ode = Eq(s*x + x*(a + x**2)*(lambda_*y(x)**2 + Derivative(y(x), x)) + (b*x**2 + c)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out