44.5.22 problem 7(d)

Internal problem ID [9178]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 7(d)
Date solved : Tuesday, September 30, 2025 at 06:12:10 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(y(x),x) = y(x)/x*tan(y(x)/x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (\ln \left (x \right )+c_1 -\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \left (-1+\tan \left (\textit {\_a} \right )\right )}d \textit {\_a} \right ) x \]

✓ Mathematica. Time used: 1.036 (sec). Leaf size: 33

ode=D[y[x],x]==y[x]/x*Tan[y[x]/x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1] (\tan (K[1])-1)}dK[1]=\log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.260 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{1} e^{- \int \limits ^{\frac {x}{y{\left (x \right )}}} \frac {\tan {\left (\frac {1}{u_{1}} \right )}}{u_{1} \left (\tan {\left (\frac {1}{u_{1}} \right )} - 1\right )}\, du_{1}} \]