19.1.2 problem 2

Internal problem ID [3516]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:40:12 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(diff(y(x),x)=y(x)^2/(x^2+1),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {1}{c_{1} -\arctan \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.170 (sec). Leaf size: 19

DSolve[D[y[x],x]==y[x]^2/(x^2+1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\arctan (x)+c_1} \\ y(x)\to 0 \\ \end{align*}