80.6.6 problem 8 (eq 69)

Internal problem ID [18570]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 8 (eq 69)
Date solved : Tuesday, January 28, 2025 at 12:00:36 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

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

\[ n \left (x \right ) = \tan \left (\frac {x^{2}}{2}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 30

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

\begin{align*} n(x)\to \tan \left (\frac {x^2}{2}+c_1\right ) \\ n(x)\to -i \\ n(x)\to i \\ \end{align*}