74.10.22 problem 22

Internal problem ID [16156]
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 : Monday, March 31, 2025 at 02:45:11 PM
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*}

✓ Maple. Time used: 0.061 (sec). Leaf size: 17

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

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

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

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

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

✓ Sympy. Time used: 0.075 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(36*y(t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): -6} 
dsolve(ode,func=y(t),ics=ics)
 

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