50.2.8 problem 1(h)

Internal problem ID [7814]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(h)
Date solved : Wednesday, March 05, 2025 at 05:06:50 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 8

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

\[ y = \sec \left (x \right ) c_{1} \]

✓ Mathematica. Time used: 0.031 (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: 0.207 (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)
 

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