30.12.24 problem 25

Internal problem ID [7616]
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 : 25
Date solved : Tuesday, September 30, 2025 at 04:54:58 PM
CAS classification : [_quadrature]

\begin{align*} 6 w^{\prime }-13 w&=0 \end{align*}

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

ode:=6*diff(w(t),t)-13*w(t) = 0; 
dsolve(ode,w(t), singsol=all);
 

\[ w = c_1 \,{\mathrm e}^{\frac {13 t}{6}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 20

ode=6*D[w[t],t]-13*w[t]==0; 
ic={}; 
DSolve[{ode,ic},w[t],t,IncludeSingularSolutions->True]
 

\begin{align*} w(t)&\to c_1 e^{13 t/6}\\ w(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
w = Function("w") 
ode = Eq(-13*w(t) + 6*Derivative(w(t), t),0) 
ics = {} 
dsolve(ode,func=w(t),ics=ics)
 

\[ w{\left (t \right )} = C_{1} e^{\frac {13 t}{6}} \]