85.70.1 problem 5 (a)

Internal problem ID [22925]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 6. Solution of linear differential equations by Laplace transform. A Exercises at page 283
Problem number : 5 (a)
Date solved : Thursday, October 02, 2025 at 09:16:40 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.081 (sec). Leaf size: 13

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)+3*y(t) = 0; 
ic:=[y(0) = 3, D(y)(0) = 5]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = {\mathrm e}^{3 t}+2 \,{\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 16

ode=D[y[t],{t,2}]-4*D[y[t],t]+3*y[t]==0; 
ic={y[0]==3,Derivative[1][y][0] ==5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.116 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): 5} 
dsolve(ode,func=y(t),ics=ics)
 

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