84.44.2 problem 37.13

Internal problem ID [22399]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 37. Second Order Boundary Value Problems. Supplementary problems
Problem number : 37.13
Date solved : Thursday, October 02, 2025 at 08:38:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y \left (\frac {\pi }{2}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 11

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

\[ y = -\frac {\sin \left (x \right ) \pi }{2}+x \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to x-\frac {1}{2} \pi \sin (x) \end{align*}

✓ Sympy. Time used: 0.031 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = x - \frac {\pi \sin {\left (x \right )}}{2} \]