82.5.5 problem 29-8

Internal problem ID [21846]
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 : 29-8
Date solved : Thursday, October 02, 2025 at 08:02:49 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 )&=0 \\ y \left (L \right )&=7 \\ \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=[y(0) = 0, y(L) = 7]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 7 \csc \left (2 L \right ) \sin \left (2 x \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 15

ode=D[y[x],{x,2}]+4*y[x]==0; 
ic={y[0]==0,y[L]==7}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 7 \csc (L) \sec (L) \sin (x) \cos (x) \end{align*}

✓ Sympy. Time used: 0.038 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {4 \sin {\left (2 x \right )}}{\sin {\left (2 L \right )}} \]