26.8.16 problem Exercise 21.20, page 231

Internal problem ID [7100]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
Problem number : Exercise 21.20, page 231
Date solved : Tuesday, September 30, 2025 at 04:21:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

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

\[ y = \frac {\left (36 \,{\mathrm e}^{3 x} c_1 +36 c_2 \,{\mathrm e}^{2 x}+6 x +5\right ) {\mathrm e}^{-x}}{36} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to \frac {1}{36} e^{-x} (6 x+5)+c_1 e^x+c_2 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{2 x} + \frac {\left (6 x + 5\right ) e^{- x}}{36} \]