49.11.9 problem 1(i)

Internal problem ID [7673]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 93
Problem number : 1(i)
Date solved : Monday, January 27, 2025 at 03:09:35 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{-x} \left (\frac {1}{60} x^{5}+c_{1} +c_{2} x +c_3 \,x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]+3*D[y[x],x]+y[x]==x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{60} e^{-x} \left (x^5+60 c_3 x^2+60 c_2 x+60 c_1\right ) \]