29.7.30 problem 205

Internal problem ID [4805]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 205
Date solved : Sunday, March 30, 2025 at 03:58:51 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: 0.457 (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]
 

\[ y(x)\to x \arcsin (-\log (x)+c_1) \]

✓ Sympy. Time used: 0.831 (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)
 

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