88.23.1 problem 1

Internal problem ID [24175]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Miscellaneous Exercises at page 162
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:00:27 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{3}+{\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

ode:=diff(diff(diff(y(x),x),x),x)-diff(y(x),x) = x^3+exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -3 x^{2}-\frac {x^{4}}{4}+{\mathrm e}^{x} c_2 -{\mathrm e}^{-x} c_1 -\frac {{\mathrm e}^{-2 x}}{6}+c_3 \]

✓ Mathematica. Time used: 0.212 (sec). Leaf size: 44

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

\begin{align*} y(x)&\to -\frac {x^4}{4}-3 x^2-\frac {e^{-2 x}}{6}+c_1 e^x-c_2 e^{-x}+c_3 \end{align*}

✓ Sympy. Time used: 0.159 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + C_{3} e^{x} - \frac {x^{4}}{4} - 3 x^{2} - \frac {e^{- 2 x}}{6} \]