64.20.3 problem 3

Internal problem ID [13575]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 3
Date solved : Monday, March 31, 2025 at 08:01:36 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Maple. Time used: 0.092 (sec). Leaf size: 8

ode:=diff(diff(y(t),t),t)-5*diff(y(t),t)+6*y(t) = 0; 
ic:=y(0) = 1, D(y)(0) = 2; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = {\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 10

ode=D[y[t],{t,2}]-5*D[y[t],t]+6*y[t]==0; 
ic={y[0]==1,Derivative[1][y][0]==2}; 
DSolve[{ode,ic},{y[t]},t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{2 t} \]

✓ Sympy. Time used: 0.167 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(6*y(t) - 5*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = e^{2 t} \]