64.11.8 problem 8

Internal problem ID [13458]
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 : 8
Date solved : Tuesday, January 28, 2025 at 05:44:18 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=5 x \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+10*y(x)=5*x*exp(-2*x),y(x), singsol=all)
 

\[ y = \frac {\left (10 \cos \left (3 x \right ) c_{1} +10 \sin \left (3 x \right ) c_{2} \right ) {\mathrm e}^{-x}}{10}+\frac {\left (5 x +1\right ) {\mathrm e}^{-2 x}}{10} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+10*y[x]==5*x*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{10} e^{-2 x} \left (5 x+10 c_2 e^x \cos (3 x)+10 c_1 e^x \sin (3 x)+1\right ) \]