32.8.10 problem Exercise 21.13, page 231

Internal problem ID [5959]
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 21.13, page 231
Date solved : Monday, January 27, 2025 at 01:28:56 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+y^{\prime }&=x^{2}+2 x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 24

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

\[ y(x)\to \frac {x^3}{3}-c_1 e^{-x}+c_2 \]