78.16.6 problem 6

Internal problem ID [18385]
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 : 6
Date solved : Tuesday, January 28, 2025 at 11:48:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \,{\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=6*exp(5*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{-x} c_{1} +\frac {{\mathrm e}^{5 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==6*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{5 x}}{2}+c_1 e^{-x}+c_2 e^{3 x} \]