Internal problem ID [3043]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 295.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-1-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 9
dsolve((x^2+1)*diff(y(x),x) = 1+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\arctan \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 25
DSolve[(1+x^2)y'[x]==(1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (\text {ArcTan}(x)+c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}