76.11.8 problem 22

Internal problem ID [17481]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.1 (Definitions and examples). Problems at page 214
Problem number : 22
Date solved : Monday, March 31, 2025 at 04:14:53 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 6

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

\[ y = \cos \left (t \right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 7

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

\[ y(t)\to \cos (t) \]

✓ Sympy. Time used: 0.056 (sec). Leaf size: 5

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

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