71.1.23 problem 37

Internal problem ID [14332]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 37
Date solved : Tuesday, January 28, 2025 at 06:26:48 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=x^{6} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x)^2=x^6,y(x), singsol=all)
 

\begin{align*} y &= \frac {x^{4}}{4}+c_{1} \\ y &= -\frac {x^{4}}{4}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[(D[y[x],x])^2==x^6,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^4}{4}+c_1 \\ y(x)\to \frac {x^4}{4}+c_1 \\ \end{align*}