20.12.3 problem Problem 18

Internal problem ID [3797]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page 575
Problem number : Problem 18
Date solved : Sunday, March 30, 2025 at 02:08:45 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-3 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+9*y(x) = 4*exp(-3*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 23

ode=D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==4*Exp[-3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (2 x^2+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.248 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 4*exp(-3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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