87.18.5 problem 5

Internal problem ID [23646]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 135
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:43:47 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+9*y(x) = 1/x^3*exp(-3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-3 x} \left (c_2 +c_1 x +\frac {1}{2 x}\right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 31

ode=D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==1/x^3*Exp[-3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.194 (sec). Leaf size: 17

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

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