Internal problem ID [13331]
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: 4.7 (g).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-y^{2}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve((x^2+1)*diff(y(x),x)=y(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: 0.208 (sec). Leaf size: 25
DSolve[(x^2+1)*y'[x]==y[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*}