23.1.211 problem 207

Internal problem ID [4818]
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 : 207
Date solved : Tuesday, September 30, 2025 at 08:42:41 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: 0.101 (sec). Leaf size: 72

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

\[ \text {Solve}\left [\int _1^x(2 K[1]+\cos (K[1] y(x)) y(x))dK[1]+\int _1^{y(x)}\left (x \cos (x K[2])-\int _1^x(\cos (K[1] K[2])-K[1] K[2] \sin (K[1] K[2]))dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✗ 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