64.12.9 problem 9

Internal problem ID [13442]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number : 9
Date solved : Monday, March 31, 2025 at 07:58:00 AM
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: 0.004 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+9*y(x) = exp(-3*x)/x^3; 
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: 0.035 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.278 (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)
 

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