67.3.13 problem Problem 14

Internal problem ID [14031]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 14
Date solved : Tuesday, January 28, 2025 at 06:13:02 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.991 (sec). Leaf size: 12

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

\[ y = -\frac {\sin \left (2 t \right ) {\mathrm e}^{t}}{2} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 14

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

\[ y(t)\to -e^t \sin (t) \cos (t) \]