Internal problem ID [5364]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {1+y^{2}+y^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(1+y(x)^2+y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (-\textit {\_Z} +x +c_{1} +\tan \left (\textit {\_Z} \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 35
DSolve[1+y[x]^2+y[x]^2*y'[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*}