85.70.8 problem 5

Internal problem ID [22932]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 6. Solution of linear differential equations by Laplace transform. A Exercises at page 283
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:16:43 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 (0\right )&=0 \\ y \left (\frac {\pi }{2}\right )&=-4 \\ \end{align*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 8

ode:=diff(diff(y(t),t),t)+y(t) = 0; 
ic:=[y(0) = 0, y(1/2*Pi) = -4]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = -4 \sin \left (t \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 9

ode=D[y[t],{t,2}]+y[t]==0; 
ic={y[0]==0,y[Pi/2]==-4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -4 \sin (t) \end{align*}

✓ Sympy. Time used: 0.042 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, y(pi/2): -4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - 4 \sin {\left (t \right )} \]