78.13.5 problem 1 (e)

Internal problem ID [18327]
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 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (e)
Date solved : Tuesday, January 28, 2025 at 11:46:42 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=20*exp(-2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}] -D[y[x],x]-6*y[x]==20*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} e^{-2 x} \left (-20 x+5 c_2 e^{5 x}-4+5 c_1\right ) \]