51.1.48 problem 48

Internal problem ID [10318]
Book : First order enumerated odes
Section : section 1
Problem number : 48
Date solved : Tuesday, September 30, 2025 at 07:19:21 PM
CAS classification : [_quadrature]

\begin{align*} x {y^{\prime }}^{n}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 5

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

\[ y = c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 15

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

\begin{align*} y(x)&\to 0^{\frac {1}{n}} x+c_1 \end{align*}

✗ Sympy

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

TypeError : cannot determine truth value of Relational: n > 1