71.1.11 problem 22 (page 30)

Internal problem ID [19187]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 22 (page 30)
Date solved : Thursday, October 02, 2025 at 03:41:30 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*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

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

\[ y = -\arcsin \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.223 (sec). Leaf size: 15

ode=(x-y[x]*Cos[y[x]/x])+x*Cos[y[x]/x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \arcsin (-\log (x)+c_1) \end{align*}

✓ Sympy. Time used: 0.565 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*cos(y(x)/x)*Derivative(y(x), x) + x - y(x)*cos(y(x)/x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = x \left (\pi - \operatorname {asin}{\left (C_{1} - \log {\left (x \right )} \right )}\right ), \ y{\left (x \right )} = x \operatorname {asin}{\left (C_{1} - \log {\left (x \right )} \right )}\right ] \]