88.23.7 problem 8

Internal problem ID [24181]
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 : 8
Date solved : Thursday, October 02, 2025 at 10:00:32 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{2 x}+{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+11*diff(y(x),x)-6*y(x) = exp(x)+exp(2*x)+exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 55

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

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

✓ Sympy. Time used: 0.208 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - exp(3*x) - exp(2*x) - exp(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)
 

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