Internal problem ID [2250]
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 40.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y-4 \,{\mathrm e}^{x} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 28
dsolve(diff(y(x),x$3)+diff(y(x),x$2)+diff(y(x),x)+y(x)=4*x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-3+2 x \right ) {\mathrm e}^{x}}{2}+\cos \relax (x ) c_{1}+\sin \relax (x ) c_{2}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 33
DSolve[y'''[x]+y''[x]+y'[x]+y[x]==4*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (x-\frac {3}{2}\right )+c_3 e^{-x}+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}