78.1.14 problem 1 (o)

Internal problem ID [18069]
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 : Tuesday, January 28, 2025 at 11:25:22 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 14

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

\[ y = \tan \left (\operatorname {RootOf}\left (-\textit {\_Z} +x +c_{1} +\tan \left (\textit {\_Z} \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 35

DSolve[1+y[x]^2+y[x]^2*D[y[x],x]==0,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*}