43.3.6 problem 2

Internal problem ID [8892]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 05:59:41 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 11

ode:=diff(y(x),x)+cos(x)*y(x) = exp(-sin(x)); 
ic:=[y(Pi) = Pi]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 52

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

\begin{align*} y(x)&\to \exp \left (\int _{\pi }^x-\cos (K[1])dK[1]\right ) \left (\int _{\pi }^x\exp \left (-\sin (K[2])-\int _{\pi }^{K[2]}-\cos (K[1])dK[1]\right )dK[2]+\pi \right ) \end{align*}

✓ Sympy. Time used: 0.600 (sec). Leaf size: 8

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

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