20.9.4 problem Problem 4

Internal problem ID [3748]
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 4
Date solved : Monday, January 27, 2025 at 07:58:07 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=2*exp(-3*x)/(x^2+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==2*Exp[-3*x]/(x^2+1),y[x],x,IncludeSingularSolutions -> True]
 

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