31.1.10 problem 3.4

Internal problem ID [5708]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 3.4
Date solved : Monday, January 27, 2025 at 01:10:51 PM
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: 0.006 (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: 0.436 (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]
 

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