22.1.10 problem 10

Internal problem ID [4316]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 07:17:40 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.281 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to x \arctan (-\log (x)+2 c_1)\\ y(x)&\to -\frac {\pi x}{2}\\ y(x)&\to \frac {\pi x}{2} \end{align*}

✗ Sympy

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

TypeError : cannot determine truth value of Relational: -1 < exp(2*_X0*I/x)