58.1.10 problem 10

Internal problem ID [9081]
Book : Second order enumerated odes
Section : section 1
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:32:13 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} {y^{\prime \prime }}^{2}&=x \end{align*}

Solution by Maple

Time used: 0.023 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)^2=x,y(x), singsol=all)
 
\begin{align*} y &= \frac {4 x^{{5}/{2}}}{15}+c_{1} x +c_{2} \\ y &= -\frac {4 x^{{5}/{2}}}{15}+c_{1} x +c_{2} \\ \end{align*}

Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 41

DSolve[(D[y[x],{x,2}])^2==x,y[x],x,IncludeSingularSolutions -> True]
 
\begin{align*} y(x)\to -\frac {4 x^{5/2}}{15}+c_2 x+c_1 \\ y(x)\to \frac {4 x^{5/2}}{15}+c_2 x+c_1 \\ \end{align*}