32.9.7 problem Exercise 22.7, page 240

Internal problem ID [5981]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number : Exercise 22.7, page 240
Date solved : Monday, January 27, 2025 at 01:29:58 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

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

\[ y \left (x \right ) = {\mathrm e}^{-x} \left (c_{2} +c_{1} x +\frac {1}{12} x^{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{12} e^{-x} \left (x^4+12 c_2 x+12 c_1\right ) \]