30.11.1 problem 1

Internal problem ID [7581]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.1 at page 156
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:54:34 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} m y^{\prime \prime }+k y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

\[ y = c_1 \sin \left (\frac {\sqrt {k}\, t}{\sqrt {m}}\right )+c_2 \cos \left (\frac {\sqrt {k}\, t}{\sqrt {m}}\right ) \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 38

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

\begin{align*} y(t)&\to c_1 \cos \left (\frac {\sqrt {k} t}{\sqrt {m}}\right )+c_2 \sin \left (\frac {\sqrt {k} t}{\sqrt {m}}\right ) \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 29

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

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