88.6.3 problem 3

Internal problem ID [23985]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:49:12 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 44

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

\[ y = \arctan \left (\frac {2 x c_1}{c_1^{2} x^{2}+1}, \frac {-c_1^{2} x^{2}+1}{c_1^{2} x^{2}+1}\right ) x \]

✓ Mathematica. Time used: 0.2 (sec). Leaf size: 52

ode=D[y[x],{x,1}]==y[x]/x+Sin[y[x]/x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x \arccos (-\tanh (\log (x)+c_1))\\ y(x)&\to x \arccos (-\tanh (\log (x)+c_1))\\ y(x)&\to 0\\ y(x)&\to -\pi x\\ y(x)&\to \pi x \end{align*}

✓ Sympy. Time used: 0.757 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = 2 x \operatorname {atan}{\left (C_{1} x \right )} \]