76.2.6 problem 6

Internal problem ID [17342]
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 : 6
Date solved : Tuesday, January 28, 2025 at 10:01:48 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(t*diff(y(t),t)+2*y(t)=sin(t),y(t), singsol=all)
 

\[ y = \frac {\sin \left (t \right )-t \cos \left (t \right )+c_{1}}{t^{2}} \]

✓ Solution by Mathematica

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

DSolve[t*D[y[t],t]+2*y[t]==Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

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