74.1.12 problem 19

Internal problem ID [15792]
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 : Tuesday, January 28, 2025 at 08:07:23 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x)+y(x)=sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 29

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

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