39.1.7 problem Problem 11.7

Internal problem ID [6512]
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
Date solved : Monday, January 27, 2025 at 02:11:06 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

\[ y = \frac {\left (-12 x -13\right ) {\mathrm e}^{-x}}{144}+{\mathrm e}^{x} c_1 +c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==2*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{144} e^{-x} (12 x+13)+c_1 e^x+c_2 e^{2 x}+c_3 e^{3 x} \]