89.3.11 problem 11

Internal problem ID [24309]
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 34
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:12:59 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 17

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

\[ x^{2} y-\tan \left (y\right ) x +c_1 = 0 \]

✓ Mathematica. Time used: 0.263 (sec). Leaf size: 47

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

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

✗ Sympy

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

Timed Out