73.7.25 problem 25

Internal problem ID [15104]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 25
Date solved : Thursday, March 13, 2025 at 05:40:07 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 10

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

\[ y = \arcsin \left (c_{1} x \right ) x \]

✓ Mathematica. Time used: 9.176 (sec). Leaf size: 19

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

\begin{align*} y(x)\to x \arcsin \left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 1.112 (sec). Leaf size: 19

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

\[ \left [ y{\left (x \right )} = x \left (\pi - \operatorname {asin}{\left (C_{1} x \right )}\right ), \ y{\left (x \right )} = x \operatorname {asin}{\left (C_{1} x \right )}\right ] \]