74.9.18 problem 29

Internal problem ID [16194]
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 : 29
Date solved : Tuesday, January 28, 2025 at 08:56:56 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=\cos \left (3 t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

dsolve([diff(diff(y(t),t),t)+9*y(t) = 0, cos(3*t), y(0) = 1, D(y)(0) = -4], singsol=all)
 

\[ y = -\frac {4 \sin \left (3 t \right )}{3}+\cos \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

DSolve[D[y[t],{t,2}]+9*y[t]==0,{y[0]==1,Derivative[1][y][0] ==-4},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \cos (3 t)-\frac {4}{3} \sin (3 t) \]