50.2.3 problem 1(c)

Internal problem ID [7809]
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(c)
Date solved : Wednesday, March 05, 2025 at 05:06:38 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);
 

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

✓ Mathematica. Time used: 0.032 (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 \cos (x) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.217 (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)
 

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