23.1.742 problem 743

Internal problem ID [5349]
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 : 743
Date solved : Tuesday, September 30, 2025 at 12:34:24 PM
CAS classification : [NONE]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 15

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

\[ y \cos \left (x \right )+x \sin \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.105 (sec). Leaf size: 59

ode=(x+Cos[x]*Sec[y[x]])D[y[x],x]+Tan[y[x]]-y[x] Sin[x]*Sec[y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

Timed Out