87.27.11 problem 18

Internal problem ID [23879]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 6. Boundary value problems. Exercise at page 262
Problem number : 18
Date solved : Thursday, October 02, 2025 at 09:46:14 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} -\frac {u^{\prime \prime }}{2}&=x \end{align*}

With initial conditions

\begin{align*} u \left (0\right )&=0 \\ u \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 13

ode:=-1/2*diff(diff(u(x),x),x) = x; 
ic:=[u(0) = 0, u(1) = 0]; 
dsolve([ode,op(ic)],u(x), singsol=all);
 

\[ u = -\frac {1}{3} x^{3}+\frac {1}{3} x \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 16

ode=-1/2*D[u[x],{x,2}]==x; 
ic={u[0]==0,u[1]==0}; 
DSolve[{ode,ic},u[x],x,IncludeSingularSolutions->True]
 

\begin{align*} u(x)&\to \frac {1}{3} \left (x-x^3\right ) \end{align*}

✗ Sympy

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

ValueError : Invalid boundary conditions for Function