Internal problem ID [13312]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.4 (d).
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: 0.0 (sec). Leaf size: 9
dsolve(diff(y(x),x)=(y(x)^2+1)/(x^2+1),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\arctan \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 25
DSolve[y'[x]==(y[x]^2+1)/(x^2+1),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*}