84.18.2 problem 10.10

Internal problem ID [22199]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 10. Linear differential equations. General remarks. Supplementary problems
Problem number : 10.10
Date solved : Thursday, October 02, 2025 at 08:34:02 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

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

\[ y = -x +c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.032 (sec). Leaf size: 14

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

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