74.9.19 problem 30

Internal problem ID [16116]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 30
Date solved : Thursday, March 13, 2025 at 07:52:13 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+49 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=\sin \left (7 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+49*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_{1} \sin \left (7 t \right )+c_{2} \cos \left (7 t \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

ode=D[y[t],{t,2}]+49*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to c_1 \cos (7 t)+c_2 \sin (7 t) \]

✓ Sympy. Time used: 0.060 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(49*y(t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} \sin {\left (7 t \right )} + C_{2} \cos {\left (7 t \right )} \]