23.3.2 problem 2

Internal problem ID [5716]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 02:02:00 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x) = x+sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{6}-\sin \left (x \right )+c_1 x +c_2 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {x^3}{6}-\sin (x)+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + \frac {x^{3}}{6} - \sin {\left (x \right )} \]