89.22.1 problem 1

Internal problem ID [24789]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Exercises at page 161
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:48:02 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=x^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-y(x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_2 +{\mathrm e}^{x} c_1 -x^{3}-6 x \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 28

ode=D[y[x],{x,2}]-y[x]== x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.049 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 - y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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