7.2.1 problem 1

Internal problem ID [19]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.3. Problems at page 27
Problem number : 1
Date solved : Tuesday, March 04, 2025 at 10:38:43 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(x),x) = -y(x)-sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\sin \left (x \right )}{2}+\frac {\cos \left (x \right )}{2}+c_1 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 25

ode=D[y[x],x]==-y[x]-Sin[x]; 
DSolve[ode,y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \left (-\sin (x)+\cos (x)+2 c_1 e^{-x}\right ) \]

✓ Sympy. Time used: 0.141 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} e^{- x} - \frac {\sin {\left (x \right )}}{2} + \frac {\cos {\left (x \right )}}{2} \]