Internal problem ID [4107]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-x^{2}-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)+diff(y(x),x)=x^2+2*x,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3}}{3}-{\mathrm e}^{-x} c_{1}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 24
DSolve[y''[x]+y'[x]==x^2+2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3}{3}-c_1 e^{-x}+c_2 \\ \end{align*}