Internal problem ID [2759]
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]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y=4 x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
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)
\[ y \left (x \right ) = c_{3} {\mathrm e}^{-x}+\cos \left (x \right ) c_{1} +x \,{\mathrm e}^{x}+\sin \left (x \right ) c_{2} -\frac {3 \,{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 36
DSolve[y'''[x]+y''[x]+y'[x]+y[x]==4*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x x-\frac {3 e^x}{2}+c_3 e^{-x}+c_1 \cos (x)+c_2 \sin (x) \]