Internal problem ID [4637]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=x^{2} {\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=x^2*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} c_{1} x +\frac {x^{4} {\mathrm e}^{-x}}{12} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 27
DSolve[y''[x]+2*y'[x]+y[x]==x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} e^{-x} \left (x^4+12 c_2 x+12 c_1\right ) \]