58.1.3 problem 3

Internal problem ID [9074]
Book : Second order enumerated odes
Section : section 1
Problem number : 3
Date solved : Monday, January 27, 2025 at 05:31:58 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

dsolve(diff(y(x),x$2)^n=0,y(x), singsol=all)
 

\[ y = c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 24

DSolve[(D[y[x],{x,2}])^n==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} 0^{\frac {1}{n}} x^2+c_2 x+c_1 \]