64.20.3 problem 3

Internal problem ID [13646]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 05:54:17 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 8.566 (sec). Leaf size: 8

dsolve([diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=0,y(0) = 1, D(y)(0) = 2],y(t), singsol=all)
 

\[ y = {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 10

DSolve[{D[y[t],{t,2}]-5*D[y[t],t]+6*y[t]==0,{y[0]==1,Derivative[1][y][0]==2}},{y[t]},t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{2 t} \]