78.1.14 problem 1 (o)

Internal problem ID [17990]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (o)
Date solved : Thursday, March 13, 2025 at 11:18:28 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.072 (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: 0.176 (sec). Leaf size: 35

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}[\text {$\#$1}-\arctan (\text {$\#$1})\&][-x+c_1] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}

✓ Sympy. Time used: 0.225 (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)
 

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