58.2.7 problem 4(c)

Internal problem ID [14548]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, section 1.3. Exercises page 22
Problem number : 4(c)
Date solved : Thursday, October 02, 2025 at 09:38:35 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 8

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

\[ y = -\sin \left (x \right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 9

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

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

✓ Sympy. Time used: 0.031 (sec). Leaf size: 7

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

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