82.5.4 problem 29-7

Internal problem ID [21845]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 29. Second Order Boundary Value Problems. Page 959
Problem number : 29-7
Date solved : Thursday, October 02, 2025 at 08:02:48 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y+y^{\prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ y \left (\pi \right )&=4 \\ \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=[y(0) = 4, y(Pi) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to 4 \cos (2 x)+c_2 \sin (2 x) \end{align*}

✗ Sympy

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

ValueError : Couldnt solve for initial conditions