Internal problem ID [4184]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter 2, Equations of the first order and degree. page 20
Problem number: 7.
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: 0.242 (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*}