88.17.3 problem 7

Internal problem ID [24114]
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. Exercises at page 127
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:59:20 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 38

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x) = exp(x)+1; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.195 (sec). Leaf size: 56

ode=D[y[x],{x,3}]-3*D[y[x],{x,1}]==Exp[x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.136 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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