44.14.17 problem 3(a)

Internal problem ID [9341]
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(a)
Date solved : Tuesday, September 30, 2025 at 06:16:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=2 x -1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)+2*y(x) = 2*x-1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -{\mathrm e}^{-2 x} c_1 +{\mathrm e}^{-x} c_2 +x -2 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.101 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + 2*y(x) + 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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