38.1.44 problem 46

Internal problem ID [8205]
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. Exercises 1.1 at page 12
Problem number : 46
Date solved : Tuesday, September 30, 2025 at 05:18:46 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=9-y^{2} \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 31

ode:=diff(y(x),x)^2 = 9-y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -3 \\ y &= 3 \\ y &= -3 \sin \left (-x +c_1 \right ) \\ y &= 3 \sin \left (-x +c_1 \right ) \\ \end{align*}

✓ Mathematica. Time used: 2.007 (sec). Leaf size: 107

ode=D[y[x],x]^2==9-y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {3 \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}}\\ y(x)&\to \frac {3 \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}}\\ y(x)&\to -\frac {3 \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}}\\ y(x)&\to \frac {3 \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}}\\ y(x)&\to -3\\ y(x)&\to 3 \end{align*}

✓ Sympy. Time used: 142.949 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 + Derivative(y(x), x)**2 - 9,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = 3 \sin {\left (C_{1} - x \right )}, \ y{\left (x \right )} = 3 \sin {\left (C_{1} + x \right )}\right ] \]