78.14.5 problem 3 (c)

Internal problem ID [18341]
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 : 3 (c)
Date solved : Tuesday, January 28, 2025 at 11:47:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=64*x*exp(-x),y(x), singsol=all)
 

\[ y = \left (-8 x^{2}+c_{1} -4 x \right ) {\mathrm e}^{-x}+{\mathrm e}^{3 x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}] -2*D[y[x],x]-3*y[x]==64*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (-8 x^2-4 x+c_2 e^{4 x}-1+c_1\right ) \]