68.1.12 problem 19

Internal problem ID [17079]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 19
Date solved : Thursday, October 02, 2025 at 01:42:46 PM
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);
 

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to e^{-x} \left (\int _1^xe^{K[1]} \sin (K[1])dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.074 (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)
 

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