74.5.55 problem 62

Internal problem ID [16019]
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 : 62
Date solved : Tuesday, January 28, 2025 at 08:26:40 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(t*diff(y(t),t)+y(t)=t*cos(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 25

DSolve[t*D[y[t],t]+y[t]==t*Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\int _1^t\cos (K[1]) K[1]dK[1]+c_1}{t} \]