57.3.8 problem 8

Internal problem ID [9065]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:31:49 PM
CAS classification : [_linear]

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

Using Laplace method With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✗ Solution by Maple

dsolve([t*diff(y(t),t)+y(t)=sin(t),y(1) = 0],y(t), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 16

DSolve[{t*D[y[t],t]+y[t]==Sin[t],y[1]==0},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\cos (1)-\cos (t)}{t} \]