29.7.29 problem 204

Internal problem ID [4804]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 204
Date solved : Sunday, March 30, 2025 at 03:58:41 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x y^{\prime }+y+2 x \sec \left (x y\right )&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 16

ode:=x*diff(y(x),x)+y(x)+2*x*sec(x*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\arcsin \left (-x^{2}+c_1 \right )}{x} \]

✓ Mathematica. Time used: 0.56 (sec). Leaf size: 19

ode=x D[y[x],x]+y[x]+2 x Sec[x y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {\arcsin \left (x^2-c_1\right )}{x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + 2*x/cos(x*y(x)) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out