49.1.4 problem 2 (a)

Internal problem ID [7583]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number : 2 (a)
Date solved : Wednesday, March 05, 2025 at 04:46:59 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

ode:=diff(y(x),x)+cos(x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{-\sin \left (x \right )} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 19

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

\begin{align*} y(x)\to c_1 e^{-\sin (x)} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.278 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} e^{- \sin {\left (x \right )}} \]