30.12.22 problem 23

Internal problem ID [7614]
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 : 23
Date solved : Tuesday, September 30, 2025 at 04:54:57 PM
CAS classification : [_quadrature]

\begin{align*} 5 y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=5*diff(y(t),t)+4*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {4 t}{5}} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 20

ode=5*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/5}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = C_{1} e^{- \frac {4 t}{5}} \]