74.10.23 problem 23

Internal problem ID [16157]
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 : 23
Date solved : Monday, March 31, 2025 at 02:45:30 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+100 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=10 \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 13

ode:=diff(diff(y(t),t),t)+100*y(t) = 0; 
ic:=y(0) = 1, D(y)(0) = 10; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \sin \left (10 t \right )+\cos \left (10 t \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 14

ode=D[y[t],{t,2}]+100*y[t]==0; 
ic={y[0]==1,Derivative[1][y][0] ==10}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \sin (10 t)+\cos (10 t) \]

✓ Sympy. Time used: 0.060 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(100*y(t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 10} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \sin {\left (10 t \right )} + \cos {\left (10 t \right )} \]