23.1.212 problem 208

Internal problem ID [4819]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 208
Date solved : Tuesday, September 30, 2025 at 08:42:49 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

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

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

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

✓ Mathematica. Time used: 0.215 (sec). Leaf size: 15

ode=x*D[y[x],x]-y[x]+x*Sec[y[x]/x]==0; 
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: 0.570 (sec). Leaf size: 22

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

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