44.3.13 problem 21 (b)

Internal problem ID [6994]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 21 (b)
Date solved : Sunday, March 30, 2025 at 11:33:22 AM
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: 0.002 (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: 0.184 (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)
 

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