15.1.3 problem 3

Internal problem ID [2843]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 3
Date solved : Monday, January 27, 2025 at 06:19:37 AM
CAS classification : [_separable]

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

dsolve((1+y(x)^2)+(1+x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.272 (sec). Leaf size: 29

DSolve[(1+y[x]^2)+(1+x^2)*D[y[x],x]==0,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*}