20.7.2 problem Problem 26

Internal problem ID [3717]
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 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 26
Date solved : Monday, January 27, 2025 at 07:55:52 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=5 x \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=5*x*exp(-2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (c_{2} +c_{1} x +\frac {5}{6} x^{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==5*x*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{-2 x} \left (5 x^3+6 c_2 x+6 c_1\right ) \]