64.12.9 problem 9

Internal problem ID [13513]
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 : Tuesday, January 28, 2025 at 05:50:48 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*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=exp(-3*x)/x^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 31

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

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