78.8.28 problem 28

Internal problem ID [18226]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 11:40:51 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 11

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

\[ y = \tanh \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.224 (sec). Leaf size: 13

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

\[ y(x)\to x \tan (\log (x)+c_1) \]