74.9.19 problem 30

Internal problem ID [16195]
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 : Tuesday, January 28, 2025 at 08:56:57 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*}

✓ Solution by Maple

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

dsolve([diff(y(t),t$2)+49*y(t)=0,sin(7*t)],singsol=all)
 

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

✓ Solution by Mathematica

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

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

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