63.1.30 problem 47

Internal problem ID [15470]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 47
Date solved : Thursday, October 02, 2025 at 10:15:45 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.052 (sec). Leaf size: 18

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

\[ y = x \operatorname {RootOf}\left (\textit {\_Z} \cos \left (\textit {\_Z} \right ) x^{2}-c_1 \right ) \]

✓ Mathematica. Time used: 0.21 (sec). Leaf size: 31

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

\[ \text {Solve}\left [-\log \left (\frac {y(x)}{x}\right )-\log \left (\cos \left (\frac {y(x)}{x}\right )\right )=2 \log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out