74.5.30 problem 30

Internal problem ID [15994]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 08:25:58 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=\frac {4}{\pi } \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 12

dsolve([t*diff(y(t),t)+y(t)=cos(t),y(1/2*Pi) = 4/Pi],y(t), singsol=all)
 

\[ y = \frac {\sin \left (t \right )+1}{t} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 25

DSolve[{t*D[y[t],t]+y[t]==Cos[t],{y[Pi/2]==4/Pi}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\int _{\frac {\pi }{2}}^t\cos (K[1])dK[1]+2}{t} \]