48.1.15 problem Example 3.16

Internal problem ID [7516]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.16
Date solved : Sunday, March 30, 2025 at 12:13:22 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(y(x),x)^2 = 4*x^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= x^{2}+c_1 \\ y &= -x^{2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 23

ode=(D[y[x],x])^2==4*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -x^2+c_1 \\ y(x)\to x^2+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.209 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**2 + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + x^{2}, \ y{\left (x \right )} = C_{1} - x^{2}\right ] \]