Internal problem ID [5452]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page
28
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \relax (x ) = \tan \left (x^{3} c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 6.156 (sec). Leaf size: 23
DSolve[x^2*y'[x]==3*(x^2+y[x]^2)*ArcTan[x,y[x]]+x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan \left (e^{-3 c_1} x^3\right ) \\ y(x)\to 0 \\ \end{align*}