88.17.6 problem 10

Internal problem ID [24117]
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 : 10
Date solved : Thursday, October 02, 2025 at 09:59:22 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x -{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 33

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+11*diff(y(x),x)-6*y(x) = x-exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {11}{36}+\frac {\left (3-2 x +4 c_3 \right ) {\mathrm e}^{3 x}}{4}+c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{2 x}-\frac {x}{6} \]

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 46

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],{x,1}]-6*y[x]==x-Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{36} (-6 x-11)+c_1 e^x+c_2 e^{2 x}+e^{3 x} \left (-\frac {x}{2}+\frac {3}{4}+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.181 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - 6*y(x) + exp(3*x) + 11*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{x} + C_{3} e^{2 x} - \frac {x}{6} + \left (C_{1} - \frac {x}{2}\right ) e^{3 x} - \frac {11}{36} \]