13.1.1 problem Example 3

Internal problem ID [2294]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 6
Problem number : Example 3
Date solved : Monday, January 27, 2025 at 05:44:51 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\sin \left (t \right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {3}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 11

dsolve([diff(y(t),t)+sin(t)*y(t)=0,y(0) = 3/2],y(t), singsol=all)
 

\[ y = \frac {3 \,{\mathrm e}^{\cos \left (t \right )-1}}{2} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 15

DSolve[{D[y[t],t]+Sin[t]*y[t]==0,y[0]==3/2},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {3}{2} e^{\cos (t)-1} \]