74.3.28 problem 23

Internal problem ID [15888]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 08:17:24 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

dsolve([t*diff(y(t),t)+y(t)=t*sin(t),y(Pi) = 1],y(t), singsol=all)
 

\[ y = \frac {\sin \left (t \right )-t \cos \left (t \right )}{t} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 24

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

\[ y(t)\to \frac {\int _{\pi }^tK[1] \sin (K[1])dK[1]+\pi }{t} \]