78.16.5 problem 5

Internal problem ID [18384]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 11:48:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-y(x)=exp(-x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 32

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

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