Internal problem ID [2645]
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: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y-x \cot \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x*diff(y(x),x)-y(x)=x*cot(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = x \arccos \left (\frac {1}{x c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 22.804 (sec). Leaf size: 48
DSolve[x*y'[x]-y[x]==x*Cot[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sec ^{-1}\left (e^{c_1} x\right ) \\ y(x)\to x \sec ^{-1}\left (e^{c_1} x\right ) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}