78.1.30 problem 2 (p)

Internal problem ID [18014]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (p)
Date solved : Monday, March 31, 2025 at 04:56:39 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 8

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

\[ y = c_1 \sec \left (x \right ) \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 15

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

\begin{align*} y(x)\to c_1 \sec (x) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = \frac {C_{1}}{\cos {\left (x \right )}} \]