76.19.3 problem 3

Internal problem ID [17727]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 5. The Laplace transform. Section 5.4 (Solving differential equations with Laplace transform). Problems at page 327
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 11:01:54 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 10.710 (sec). Leaf size: 13

dsolve([diff(y(t),t$2)-8*diff(y(t),t)+25*y(t)=0,y(0) = 0, D(y)(0) = 3],y(t), singsol=all)
 

\[ y = {\mathrm e}^{4 t} \sin \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 15

DSolve[{D[y[t],{t,2}]-8*D[y[t],t]+25*y[t]==0,{y[0]==0,Derivative[1][y][0] == 3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{4 t} \sin (3 t) \]