46.7.1 problem 18

Internal problem ID [7362]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:51:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.234 (sec). Leaf size: 10

dsolve([9*diff(y(t),t$2)-6*diff(y(t),t)+y(t)=0,y(0) = 3, D(y)(0) = 1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 14

DSolve[{9*D[y[t],{t,2}]-6*D[y[t],t]+y[t]==0,{y[0]==3,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 e^{t/3} \]