85.69.7 problem 7 (a)

Internal problem ID [22923]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 217
Problem number : 7 (a)
Date solved : Thursday, October 02, 2025 at 09:16:39 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=f \left (x \right ) \end{align*}

With initial conditions

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to (x-1) \int _1^0\int _1^{K[2]}f(K[1])dK[1]dK[2]+\int _1^x\int _1^{K[2]}f(K[1])dK[1]dK[2] \end{align*}

✓ Sympy. Time used: 0.213 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} + x \left (C_{2} + \int f{\left (x \right )}\, dx\right ) - \int x f{\left (x \right )}\, dx \]