57.1.48 problem 48

Internal problem ID [9032]
Book : First order enumerated odes
Section : section 1
Problem number : 48
Date solved : Monday, January 27, 2025 at 05:27:41 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

\[ y = c_{1} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 15

DSolve[x*(D[y[x],x])^n==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 0^{\frac {1}{n}} x+c_1 \]