Internal problem ID [11837]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=\frac {{\mathrm e}^{-3 x}}{x^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-3 x} \left (2 c_{1} x^{2}+2 c_{2} x +1\right )}{2 x} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 31
DSolve[y''[x]+6*y'[x]+9*y[x]==Exp[-3*x]/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-3 x} \left (2 c_2 x^2+2 c_1 x+1\right )}{2 x} \]