74.1.41 problem 48

Internal problem ID [15821]
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 : 48
Date solved : Tuesday, January 28, 2025 at 08:08:11 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 19

dsolve([diff(y(t),t)+y(t)=sin(t),y(0) = -1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 28

DSolve[{D[y[t],t]+y[t]==Sin[t],{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (\int _0^te^{K[1]} \sin (K[1])dK[1]-1\right ) \]