78.1.8 problem 1 (i)

Internal problem ID [18063]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (i)
Date solved : Tuesday, January 28, 2025 at 11:24:27 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.186 (sec). Leaf size: 12

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

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