17.6.6 problem 1.2-1 (f)

Internal problem ID [3443]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (f)
Date solved : Monday, January 27, 2025 at 07:36:52 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 19

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

\[ y(t)\to \frac {\sin (t)-t \cos (t)+c_1}{t^2} \]