Internal problem ID [3155]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve((x*cos(y(x)/x)^2-y(x))+x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\arctan \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.5 (sec). Leaf size: 37
DSolve[(x*Cos[y[x]/x]^2-y[x])+x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \arctan (-\log (x)+2 c_1) y(x)\to -\frac {\pi x}{2} y(x)\to \frac {\pi x}{2} \end{align*}