74.2.2 problem 7

Internal problem ID [15843]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 08:09:19 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: 17

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 29

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

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