85.4.1 problem 1 (a)

Internal problem ID [22442]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. Section 1.3. A Exercises at page 21
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 08:39:30 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\pi \right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 8

ode:=diff(y(x),x)+y(x)*tan(x) = 0; 
ic:=[y(Pi) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -4 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 9

ode=D[y[x],x]+y[x]*Tan[x]==0; 
ic={y[Pi]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -4 \cos (x) \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*tan(x) + Derivative(y(x), x),0) 
ics = {y(pi): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 4 \cos {\left (x \right )} \]