28.1.10 problem 10

Internal problem ID [4316]
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
Date solved : Monday, January 27, 2025 at 09:02:00 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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: 0.457 (sec). Leaf size: 37

DSolve[(x*Cos[y[x]/x]^2-y[x])+x*D[y[x],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*}