20.9.2 problem Problem 2

Internal problem ID [3746]
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
Date solved : Monday, January 27, 2025 at 07:58:02 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=x^(-2)*exp(-2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==x^(-2)*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} (-\log (x)+c_2 x-1+c_1) \]