74.10.8 problem 8

Internal problem ID [16134]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 8
Date solved : Thursday, March 13, 2025 at 07:52:38 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+9 y&=0 \end{align*}

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

ode:=4*diff(diff(y(t),t),t)+9*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_{1} \sin \left (\frac {3 t}{2}\right )+c_{2} \cos \left (\frac {3 t}{2}\right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 24

ode=4*D[y[t],{t,2}]+9*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to c_1 \cos \left (\frac {3 t}{2}\right )+c_2 \sin \left (\frac {3 t}{2}\right ) \]

✓ Sympy. Time used: 0.056 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*y(t) + 4*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} \sin {\left (\frac {3 t}{2} \right )} + C_{2} \cos {\left (\frac {3 t}{2} \right )} \]