Internal problem ID [5238]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 89
Problem number: 1(a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 38
dsolve(diff(y(x),x$3)-y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = -x +c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 52
DSolve[y'''[x]-y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+c_1 e^x+e^{-x/2} \left (c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_3 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}