65.1.23 problem 37

Internal problem ID [15619]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 37
Date solved : Thursday, October 02, 2025 at 10:21:12 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\begin{align*} y &= \frac {x^{4}}{4}+c_1 \\ y &= -\frac {x^{4}}{4}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 29

ode=(D[y[x],x])^2==x^6; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**6 + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + \frac {x^{4}}{4}, \ y{\left (x \right )} = C_{1} - \frac {x^{4}}{4}\right ] \]