68.18.47 problem 54 (a)

Internal problem ID [17891]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 54 (a)
Date solved : Thursday, October 02, 2025 at 02:29:18 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)-4*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{5 t}+c_1 \right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

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

\begin{align*} y(t)&\to c_1 e^{-4 t}+c_2 e^t \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 14

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 = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 4 t} + C_{2} e^{t} \]