89.7.7 problem 7

Internal problem ID [24438]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:31:57 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (3 \tan \left (x \right )-2 \cos \left (y\right )\right ) \sec \left (x \right )^{2}+\tan \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 14

ode:=(3*tan(x)-2*cos(y(x)))*sec(x)^2+tan(x)*sin(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arccos \left (\tan \left (x \right )+c_1 \cot \left (x \right )^{2}\right ) \]

✓ Mathematica. Time used: 105.314 (sec). Leaf size: 35

ode=(3*Tan[x]-2*Cos[y[x]] )*Sec[x]^2+( Tan[x]*Sin[ y[x]] )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\arccos \left (\tan (x)-6 c_1 \cot ^2(x)\right )\\ y(x)&\to \arccos \left (\tan (x)-6 c_1 \cot ^2(x)\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*cos(y(x)) + 3*tan(x))*sec(x)**2 + sin(y(x))*tan(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out