Internal problem ID [1872]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {1+y^{2}+\left (x^{2}+1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve((1+y(x)^2)+(1+x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\tan \left (\arctan \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 29
DSolve[(1+y[x]^2)+(1+x^2)*y'[x]==0,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*}