29.11.4 problem 295

Internal problem ID [4895]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 295
Date solved : Monday, January 27, 2025 at 09:46:47 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

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

\[ y \left (x \right ) = \tan \left (\arctan \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 25

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