Internal problem ID [2242]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 31.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y-9 \,{\mathrm e}^{-x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=9*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {9 \,{\mathrm e}^{-x}}{4}+c_{1} \cos \left (x \right )+{\mathrm e}^{x} c_{2} +c_{3} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[y'''[x]-y''[x]+y'[x]-y[x]==9*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {9 e^{-x}}{4}+c_3 e^x+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}