Internal problem ID [13131]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{2}-y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve(y(x)^2+1-diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 24
DSolve[y[x]^2+1-y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (x+c_1) y(x)\to -i y(x)\to i \end{align*}