Internal problem ID [10865]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 2, First Order Equations. Problems page 149
Problem number: Problem 1(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{2} y^{\prime }-y^{2}-1=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x^2*diff(y(x),x)=1+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\frac {c_{1} x -1}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.247 (sec). Leaf size: 30
DSolve[x^2*y'[x]==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {-1+c_1 x}{x}\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}