84.28.7 problem 16.11

Internal problem ID [22284]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 16. Initial-value problems. Supplementary problems
Problem number : 16.11
Date solved : Thursday, October 02, 2025 at 08:37:04 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 5

ode:=diff(diff(y(x),x),x)+y(x) = 0; 
ic:=[y(2) = 0, D(y)(2) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 6

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

\begin{align*} y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.032 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = 0 \]