6.5.21 problem 18

Internal problem ID [1645]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 18
Date solved : Tuesday, September 30, 2025 at 04:41:13 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.245 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to x \arcsin (\log (x)+c_1) \end{align*}

✓ Sympy. Time used: 0.563 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/cos(y(x)/x) - y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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