23.1.743 problem 746

Internal problem ID [5350]
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 : 746
Date solved : Tuesday, September 30, 2025 at 12:35:09 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

ode:=(1+(x+y(x))*tan(y(x)))*diff(y(x),x)+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.172 (sec). Leaf size: 41

ode=(1+(x+y[x])*Tan[y[x]])*D[y[x],x]+1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(((x + y(x))*tan(y(x)) + 1)*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out