61.2.11 problem 11

Internal problem ID [11938]
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 : 11
Date solved : Sunday, March 30, 2025 at 09:23:59 PM
CAS classification : [_Riccati]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 1155

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

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

✓ Mathematica. Time used: 1.303 (sec). Leaf size: 1384

ode=D[y[x],x]==(a*x^(2*n)+b*x^(n-1))*y[x]^2+c; 
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") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-c - (a*x**(2*n) + b*x**(n - 1))*y(x)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -a*x**(2*n)*y(x)**2 - b*x**(n - 1)*y(x)**2 - c + Derivative(y(x), x) cannot be solved by the factorable group method