67.15.62 problem 22.12 (g)

Internal problem ID [16780]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.12 (g)
Date solved : Thursday, October 02, 2025 at 01:38:46 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=6 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)+diff(y(x),x)-y(x) = 6*exp(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 27

ode=D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==6*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.095 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - 6*exp(x) + Derivative(y(x), x) - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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