Internal problem ID [2266]
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 8.7, The Variation of Parameters
Method. page 556
Problem number: Problem 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+4 y-\frac {{\mathrm e}^{-2 x}}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=x^(-2)*exp(-2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{-2 x} x c_{1}-\left (\ln \relax (x )+1\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 23
DSolve[y''[x]+4*y'[x]+4*y[x]==x^(-2)*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} (-\log (x)+c_2 x-1+c_1) \\ \end{align*}