38.5.70 problem 59

Internal problem ID [8418]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 59
Date solved : Tuesday, September 30, 2025 at 05:36:11 PM
CAS classification : [_quadrature]

\begin{align*} y^{2}+{y^{\prime }}^{2}&=1 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 29

ode:=y(x)^2+diff(y(x),x)^2 = 1; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -1 \\ y &= 1 \\ y &= -\sin \left (-x +c_1 \right ) \\ y &= \sin \left (-x +c_1 \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 41

ode=y[x]^2+D[y[x],x]^2==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sin (x-c_1)\\ y(x)&\to \sin (x+c_1)\\ y(x)&\to -1\\ y(x)&\to 1\\ y(x)&\to \text {Interval}[\{-1,1\}] \end{align*}

✓ Sympy. Time used: 119.117 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 + Derivative(y(x), x)**2 - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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