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 : Wednesday, March 05, 2025 at 05:35:29 AM
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*}

✓ Maple. Time used: 0.572 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+13*y(t) = 0; 
ic:=y(0) = 0, D(y)(0) = -3; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.226 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(13*y(t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): -3} 
dsolve(ode,func=y(t),ics=ics)
 

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