78.4.1 problem 3.a

Internal problem ID [21029]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 5, Laplace transforms. Problems section 5.7
Problem number : 3.a
Date solved : Thursday, October 02, 2025 at 07:01:35 PM
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 )&=2 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.110 (sec). Leaf size: 17

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

\[ y = 6 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{3 t} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to -2 e^{2 t} \left (2 e^t-3\right ) \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 14

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): 2, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (6 - 4 e^{t}\right ) e^{2 t} \]