84.38.14 problem 26.26

Internal problem ID [22368]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 26. Solutions of linear differential equations with constant coefficients by Laplace transform. Supplementary problems
Problem number : 26.26
Date solved : Thursday, October 02, 2025 at 08:38:00 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 6

ode:=diff(diff(y(t),t),t)+y(t) = 0; 
ic:=[y(Pi) = 0, D(y)(Pi) = -1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 7

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

\begin{align*} y(t)&\to \sin (t) \end{align*}

✓ Sympy. Time used: 0.027 (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(pi): 0, Subs(Derivative(y(t), t), t, pi): -1} 
dsolve(ode,func=y(t),ics=ics)
 

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