64.12.17 problem 17

Internal problem ID [13521]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 05:51:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

\[ y = \left (-\int {\mathrm e}^{-x} \left (\operatorname {Ei}_{1}\left (-x \right )-c_{1} \right )d x +c_{2} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 43

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

\[ y(x)\to e^{-2 x} \left (\int _1^x-\frac {e^{K[1]}}{K[1]}dK[1]+e^x \log (x)+c_2 e^x+c_1\right ) \]