50.14.18 problem 3(b)

Internal problem ID [8056]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 3(b)
Date solved : Sunday, March 30, 2025 at 12:41:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 29

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

\[ y(x)\to \frac {e^{-x}}{6}+c_1 e^x+c_2 e^{2 x} \]

✓ Sympy. Time used: 0.207 (sec). Leaf size: 20

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

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