77.1.11 problem 22 (page 30)

Internal problem ID [17901]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 22 (page 30)
Date solved : Tuesday, January 28, 2025 at 11:11:43 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: 0.006 (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)
 

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

✓ Solution by Mathematica

Time used: 0.747 (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]
 

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