12.3.23 problem 24

Internal problem ID [1600]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 24
Date solved : Monday, January 27, 2025 at 05:13:11 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 9

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

\[ y = \tan \left (\arctan \left (x \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.239 (sec). Leaf size: 25

DSolve[D[y[x],x]==(1+y[x]^2)/(1+x^2),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*}