61.2.33 problem 33

Internal problem ID [11960]
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 : 33
Date solved : Sunday, March 30, 2025 at 09:29:06 PM
CAS classification : [_Riccati]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed Out