80.2.5 problem 6

Internal problem ID [18544]
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 24. Problems at page 62
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 11:55:19 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 18

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

\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (\ln \left (x \right )+x -\tan \left (\textit {\_Z} \right )-\textit {\_Z} +c_{1} \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.304 (sec). Leaf size: 19

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

\[ y(x)\to \text {InverseFunction}[\arctan (\text {$\#$1})+\text {$\#$1}\&][x+\log (x)+c_1] \]