74.10.22 problem 22

Internal problem ID [16227]
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 : 22
Date solved : Tuesday, January 28, 2025 at 08:57:50 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+36 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+36*y(t)=0,y(0) = 2, D(y)(0) = -6],y(t), singsol=all)
 

\[ y = -\sin \left (6 t \right )+2 \cos \left (6 t \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]+36*y[t]==0,{y[0]==2,Derivative[1][y][0] ==-6}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 \cos (6 t)-\sin (6 t) \]