78.9.11 problem 5 (e)

Internal problem ID [18259]
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 14. Introduction. Problems at page 112
Problem number : 5 (e)
Date solved : Tuesday, January 28, 2025 at 11:44:36 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 24

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

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