Internal problem ID [5252]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y-x^{2} {\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
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)
\[ y \relax (x ) = \frac {x^{5} {\mathrm e}^{-x}}{60}+{\mathrm e}^{-x} c_{1}+c_{2} x \,{\mathrm e}^{-x}+c_{3} x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[y'''[x]+3*y''[x]+3*y'[x]+y[x]==x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{60} e^{-x} \left (x^5+60 c_3 x^2+60 c_2 x+60 c_1\right ) \\ \end{align*}