78.3.3 problem 1 (c)

Internal problem ID [18106]
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 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (c)
Date solved : Tuesday, January 28, 2025 at 11:27:38 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 12

dsolve(x^2*diff(y(x),x)=3*(x^2+y(x)^2)*arctan(y(x)/x)+x*y(x),y(x), singsol=all)
 

\[ y = \tan \left (c_1 \,x^{3}\right ) x \]

✓ Solution by Mathematica

Time used: 1.250 (sec). Leaf size: 16

DSolve[x^2*D[y[x],x]==3*(x^2+y[x]^2)*ArcTan[y[x]/x]+x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \tan \left (e^{c_1} x^3\right ) \]