Internal problem ID [2036]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.4, page 36
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{2}}{x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 14
dsolve(diff(y(x),x)=y(x)^2/(x^2+1),y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{\arctan \relax (x )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.144 (sec). Leaf size: 19
DSolve[y'[x]==y[x]^2/(x^2+1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\text {ArcTan}(x)+c_1} \\ y(x)\to 0 \\ \end{align*}