46.6.2 problem 2

Internal problem ID [7348]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:50:50 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+2 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.191 (sec). Leaf size: 10

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

\[ y = \frac {3 \,{\mathrm e}^{-2 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 31

DSolve[{D[y[t],t]+52/10*y[t]==194/10*Sin[2*t],{y[0]==15/10}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} \left (11 e^{-26 t/5}+13 \sin (2 t)-5 \cos (2 t)\right ) \]