30.12.1 problem 1

Internal problem ID [7593]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:54:44 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \end{align*}

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

ode:=2*diff(diff(y(t),t),t)+7*diff(y(t),t)-4*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{\frac {9 t}{2}}+c_2 \right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 24

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

\begin{align*} y(t)&\to e^{-4 t} \left (c_1 e^{9 t/2}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 15

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

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