54.1.356 problem 363

Internal problem ID [11670]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 363
Date solved : Tuesday, September 30, 2025 at 10:05:54 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} \left (x y^{\prime }-y\right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 32

ode:=(-y(x)+x*diff(y(x),x))*cos(y(x)/x)^2+x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {-x \sin \left (\frac {2 y}{x}\right )-2 y}{4 x}-\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.156 (sec). Leaf size: 33

ode=x + Cos[y[x]/x]^2*(-y[x] + x*D[y[x],x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {y(x)}{2 x}+\frac {1}{4} \sin \left (\frac {2 y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (x*Derivative(y(x), x) - y(x))*cos(y(x)/x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : cannot determine truth value of Relational: 2*x < -4*x/(exp(2*_X0*I/x) + 2*exp(_X0*I/x)