28.1.116 problem 139

Internal problem ID [4422]
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 : 139
Date solved : Monday, January 27, 2025 at 09:16:42 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

dsolve((x-y(x)*cos( y(x)/x ))+(x*cos( y(x)/x) )*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\arcsin \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.387 (sec). Leaf size: 15

DSolve[(x-y[x]*Cos[ y[x]/x ])+(x*Cos[ y[x]/x] )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \arcsin (-\log (x)+c_1) \]