44.1.14 problem 1(o)

Internal problem ID [9072]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 1(o)
Date solved : Tuesday, September 30, 2025 at 06:03:44 PM
CAS classification : [_quadrature]

\begin{align*} 1+y^{2}+y^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 14

ode:=1+y(x)^2+y(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tan \left (\operatorname {RootOf}\left (-\textit {\_Z} +x +c_1 +\tan \left (\textit {\_Z} \right )\right )\right ) \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 48

ode=1+y[x]^2+y[x]^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]^2}{K[1]^2+1}dK[1]\&\right ][-x+c_1]\\ y(x)&\to -i\\ y(x)&\to i \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 10

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

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