28.1.9 problem 9

Internal problem ID [4315]
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
Date solved : Monday, January 27, 2025 at 09:01:54 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }-y&=x \cot \left (\frac {y}{x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 14

dsolve(x*diff(y(x),x)-y(x)=x*cot(y(x)/x),y(x), singsol=all)
 

\[ y \left (x \right ) = x \arccos \left (\frac {1}{c_{1} x}\right ) \]

✓ Solution by Mathematica

Time used: 24.202 (sec). Leaf size: 56

DSolve[x*D[y[x],x]-y[x]==x*Cot[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \arccos \left (\frac {e^{-c_1}}{x}\right ) \\ y(x)\to x \arccos \left (\frac {e^{-c_1}}{x}\right ) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}