67.3.14 problem Problem 15

Internal problem ID [13961]
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 15
Date solved : Monday, March 31, 2025 at 08:20:20 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-20 y^{\prime }+51 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-14 \end{align*}

✓ Maple. Time used: 0.100 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)-20*diff(y(t),t)+51*y(t) = 0; 
ic:=y(0) = 0, D(y)(0) = -14; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = -2 \,{\mathrm e}^{10 t} \sinh \left (7 t \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

ode=D[y[t],{t,2}]-20*D[y[t],t]+51*y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==-14}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{3 t}-e^{17 t} \]

✓ Sympy. Time used: 0.176 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(51*y(t) - 20*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): -14} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (1 - e^{14 t}\right ) e^{3 t} \]