Internal problem ID [5172]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1.6 Introduction– Linear equations of First Order. Page 41
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {-2 y+y^{\prime }-x^{2}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
dsolve(diff(y(x),x)-2*y(x)=x^2+x,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x^{2}}{2}-x -\frac {1}{2}+{\mathrm e}^{2 x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 23
DSolve[y'[x]-2*y[x]==x^2+x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} (x+1)^2+c_1 e^{2 x} \\ \end{align*}