Internal problem ID [2646]
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]
Solve \begin {gather*} \boxed {x \left (\cos ^{2}\left (\frac {y}{x}\right )\right )-y+y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve((x*cos(y(x)/x)^2-y(x))+x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\arctan \left (c_{1}+\ln \relax (x )\right ) x \]
✓ Solution by Mathematica
Time used: 0.45 (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 \text {ArcTan}(-\log (x)+2 c_1) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}