46.6.1 problem 1

Internal problem ID [7347]
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 : 1
Date solved : Monday, January 27, 2025 at 02:50:49 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+\frac {26 y}{5}&=\frac {97 \sin \left (2 t \right )}{5} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.280 (sec). Leaf size: 23

dsolve([diff(y(t),t)+52/10*y(t)=194/10*sin(2*t),y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {5 \,{\mathrm e}^{-\frac {26 t}{5}}}{4}-\frac {5 \cos \left (2 t \right )}{4}+\frac {13 \sin \left (2 t \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 31

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

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