25.2.9 problem 10

Internal problem ID [6865]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 03:56:09 PM
CAS classification : [_Riccati]

\begin{align*} \frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1}&=0 \end{align*}

✗ Maple

ode:=x^n/(b*y(x)^2-c*x^(2*a))*diff(y(x),x)-a*y(x)*x^(a-1)/(b*y(x)^2-c*x^(2*a))+x^(a-1) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : The given ODE Derivative(y(x), x) - (a*x**(a - 1)*y(x) - b*x**(a - 1)*y(x)**2 + c*x**(3*a - 1))/x**n cannot be solved by the factorable group method