Internal problem ID [950]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1+y^{2}}{x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 9
dsolve(diff(y(x),x)=(1+y(x)^2)/(1+x^2),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\arctan \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.241 (sec). Leaf size: 25
DSolve[y'[x]==(1+y[x]^2)/(1+x^2),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*}