87.22.3 problem 3

Internal problem ID [23748]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 4. The Laplace transform. Exercise at page 199
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:44:52 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 13

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

\[ y = -{\mathrm e}^{t}+{\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 16

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

\begin{align*} y(t)&\to e^{-4 t}-e^t \end{align*}

✓ Sympy. Time used: 0.119 (sec). Leaf size: 12

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

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