32.8.15 problem Exercise 21.19, page 231

Internal problem ID [5964]
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
Date solved : Monday, January 27, 2025 at 01:29:13 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

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

\[ y \left (x \right ) = \frac {7}{4}+\left (-x -1-c_{1} \right ) {\mathrm e}^{-2 x}+\frac {x^{2}}{2}+c_{2} {\mathrm e}^{-x}-\frac {3 x}{2} \]

✓ Solution by Mathematica

Time used: 0.133 (sec). Leaf size: 41

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

\[ y(x)\to \frac {1}{4} \left (2 x^2-6 x+7\right )+e^{-2 x} (-x-1+c_1)+c_2 e^{-x} \]