64.11.10 problem 10

Internal problem ID [13460]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 05:44:32 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y&=8 x \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 32

dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=8*x*exp(-2*x),y(x), singsol=all)
 

\[ y = \frac {\left (2 \cos \left (x \right ) c_{2} +2 c_{3} \sin \left (x \right )-4 x -1\right ) {\mathrm e}^{-2 x}}{2}+{\mathrm e}^{2 x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 40

DSolve[D[y[x],{x,3}]+2*D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==8*x*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-2 x} \left (-4 x+2 c_3 e^{4 x}+2 c_2 \cos (x)+2 c_1 \sin (x)-1\right ) \]