46.6.6 problem 6

Internal problem ID [7352]
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 : 6
Date solved : Monday, January 27, 2025 at 02:50:53 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=29 \cos \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {16}{5}}\\ y^{\prime }\left (0\right )&={\frac {31}{5}} \end{align*}

✓ Solution by Maple

Time used: 0.267 (sec). Leaf size: 25

dsolve([diff(y(t),t$2)-6*diff(y(t),t)+5*y(t)=29*cos(2*t),y(0) = 16/5, D(y)(0) = 31/5],y(t), singsol=all)
 

\[ y = {\mathrm e}^{t}+\frac {\cos \left (2 t \right )}{5}-\frac {12 \sin \left (2 t \right )}{5}+2 \,{\mathrm e}^{5 t} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 32

DSolve[{D[y[t],{t,2}]-6*D[y[t],t]+5*y[t]==29*Cos[2*t],{y[0]==32/10,Derivative[1][y][0] ==62/10}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t+2 e^{5 t}-\frac {12}{5} \sin (2 t)+\frac {1}{5} \cos (2 t) \]