34.2.7 problem 7

Internal problem ID [6037]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 2, Equations of the first order and degree. page 20
Problem number : 7
Date solved : Monday, January 27, 2025 at 01:34:08 PM
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)=(y(x)^2+1)/(x^2+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.274 (sec). Leaf size: 25

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