50.1.14 problem 1(o)

Internal problem ID [7786]
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 : Monday, January 27, 2025 at 03:23:09 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.019 (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: 0.187 (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*}