Internal problem ID [4661]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page
95
Problem number: Problem 11.7.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y-2 x \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=2*x*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (12 x +13\right ) {\mathrm e}^{-x}}{144}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 42
DSolve[y'''[x]-6*y''[x]+11*y'[x]-6*y[x]==2*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{144} e^{-x} (12 x+13)+c_1 e^x+c_2 e^{2 x}+c_3 e^{3 x} \\ \end{align*}