67.18.10 problem 27.1 (j)

Internal problem ID [16881]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page 496
Problem number : 27.1 (j)
Date solved : Thursday, October 02, 2025 at 01:40:05 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=7 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.093 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)-5*diff(y(t),t)+6*y(t) = 7; 
ic:=[y(0) = 2, D(y)(0) = 4]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = -\frac {3 \,{\mathrm e}^{2 t}}{2}+\frac {7}{6}+\frac {7 \,{\mathrm e}^{3 t}}{3} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 25

ode=D[y[t],{t,2}]-5*D[y[t],t]+6*y[t]==7; 
ic={y[0]==2,Derivative[1][y][0] ==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{6} \left (-9 e^{2 t}+14 e^{3 t}+7\right ) \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(6*y(t) - 5*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 7,0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {7 e^{3 t}}{3} - \frac {3 e^{2 t}}{2} + \frac {7}{6} \]