55.2.76 problem 76

Internal problem ID [13302]
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 : 76
Date solved : Wednesday, October 01, 2025 at 06:34:07 AM
CAS classification : [_rational, _Riccati]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=(a*x^n+b*x^m+c)*D[y[x],x]==a*x^(n-2)*y[x]^2+b*x^(m-1)*y[x]+c; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
m = symbols("m") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-a*x**(n - 2)*y(x)**2 - b*x**(m - 1)*y(x) - c + (a*x**n + b*x**m + c)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out