78.5.16 problem 4 (e)

Internal problem ID [18159]
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. Section 9 (Integrating Factors). Problems at page 80
Problem number : 4 (e)
Date solved : Tuesday, January 28, 2025 at 11:34:32 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x y^{\prime }&=y+x^{2}+9 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(x*diff(y(x),x)= y(x)+x^2+9*y(x)^2,y(x), singsol=all)
 

\[ y = \frac {\tan \left (3 x +3 c_1 \right ) x}{3} \]

✓ Solution by Mathematica

Time used: 0.245 (sec). Leaf size: 17

DSolve[x*D[y[x],x] == y[x]+x^2+9*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} x \tan (3 (x+c_1)) \]