Internal problem ID [4112]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.19, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-{\mathrm e}^{-2 x}-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(-2*x)+x^2,y(x), singsol=all)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-2 x}-\frac {3 x}{2}+\frac {7}{4}-{\mathrm e}^{-2 x} x -{\mathrm e}^{-2 x}+\frac {x^{2}}{2}+c_{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 38
DSolve[y''[x]+3*y'[x]+2*y[x]==Exp[-2*x]+x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (x-3) x+e^{-2 x} (-x-1+c_1)+c_2 e^{-x}+\frac {7}{4} \\ \end{align*}