89.4.17 problem 18

Internal problem ID [24339]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 39
Problem number : 18
Date solved : Thursday, October 02, 2025 at 10:19:55 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 38

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

\begin{align*} y &= \frac {\arctan \left (\sqrt {{\mathrm e}^{-2 x} c_1 -1}\right )}{x} \\ y &= -\frac {\arctan \left (\sqrt {{\mathrm e}^{-2 x} c_1 -1}\right )}{x} \\ \end{align*}

✓ Mathematica. Time used: 60.105 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to -\frac {\arccos \left (e^{x-c_1}\right )}{x}\\ y(x)&\to \frac {\arccos \left (e^{x-c_1}\right )}{x} \end{align*}

✗ Sympy

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

Timed Out