52.8.13 problem 15(a)

Internal problem ID [8377]
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. EXERCISES 7.5. Page 315
Problem number : 15(a)
Date solved : Sunday, March 30, 2025 at 12:53:23 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 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*}

✓ Maple. Time used: 0.126 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+10*y(t) = 0; 
ic:=y(0) = 0, D(y)(0) = 1; 
dsolve([ode,ic],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 18

ode=D[y[t],{t,2}]+2*D[y[t],t]+10*y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{3} e^{-t} \sin (3 t) \]

✓ Sympy. Time used: 0.182 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(10*y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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