Internal problem ID [5389]
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 1.3 SEPARABLE EQUATIONS. Page
12
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+1+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 11
dsolve((1+x^2)*diff(y(x),x)+1+y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\tan \left (\arctan \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 29
DSolve[(1+x^2)*y'[x]+1+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\tan (\text {ArcTan}(x)-c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}