46.6.8 problem 8

Internal problem ID [7354]
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 : 8
Date solved : Monday, January 27, 2025 at 02:50:54 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {81}{10}}\\ y^{\prime }\left (0\right )&={\frac {39}{10}} \end{align*}

✓ Solution by Maple

Time used: 0.230 (sec). Leaf size: 15

dsolve([diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=0,y(0) = 81/10, D(y)(0) = 39/10],y(t), singsol=all)
 

\[ y = -\frac {3 \left (41 t -27\right ) {\mathrm e}^{2 t}}{10} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]-4*D[y[t],t]+4*y[t]==0,{y[0]==81/10,Derivative[1][y][0] ==39/10}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {3}{10} e^{2 t} (41 t-27) \]