76.2.33 problem 41

Internal problem ID [17369]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 41
Date solved : Tuesday, January 28, 2025 at 10:03:17 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{t}&=3 \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(y(t),t)+1/t*y(t)=3*cos(2*t),y(t), singsol=all)
 

\[ y = \frac {4 c_{1} +6 \sin \left (2 t \right ) t +3 \cos \left (2 t \right )}{4 t} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 28

DSolve[D[y[t],t]+1/t*y[t]==3*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\int _1^t3 \cos (2 K[1]) K[1]dK[1]+c_1}{t} \]