52.6.7 problem 27

Internal problem ID [8342]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number : 27
Date solved : Monday, January 27, 2025 at 03:49:15 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 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: 0.572 (sec). Leaf size: 14

dsolve([diff(y(t),t$2)-6*diff(y(t),t)+13*y(t)=0,y(0) = 0, D(y)(0) = -3],y(t), singsol=all)
 

\[ y = -\frac {3 \,{\mathrm e}^{3 t} \sin \left (2 t \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 16

DSolve[{D[y[t],{t,2}]-6*D[y[t],t]+13*y[t]==0,{y[0]==0,Derivative[1][y][0] ==-3}},y[t],t,IncludeSingularSolutions -> True]
 

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