29.14.4 problem 384

Internal problem ID [4983]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 384
Date solved : Sunday, March 30, 2025 at 04:27:57 AM
CAS classification : [_Riccati]

\begin{align*} x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 1156

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

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

✗ Mathematica

ode=x^n*D[y[x],x]+x^(2*n-2)+y[x]^2+(1-n)*x^(n-1)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

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