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]
\[ \boxed {y^{\prime }-\frac {1+y^{2}}{x^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 9
dsolve(diff(y(x),x)=(1+y(x)^2)/(1+x^2),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\arctan \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.227 (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 (\arctan (x)+c_1) y(x)\to -i y(x)\to i \end{align*}