78.14.2 problem 2

Internal problem ID [18338]
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 19. The Method of Variation of Parameters. Problems at page 135
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 11:47:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=exp(-x),y(x), singsol=all)
 

\[ y = \frac {\left (4 c_{2} {\mathrm e}^{5 x}-{\mathrm e}^{x}+4 c_{1} \right ) {\mathrm e}^{-2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 31

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

\[ y(x)\to -\frac {e^{-x}}{4}+c_1 e^{-2 x}+c_2 e^{3 x} \]