78.9.5 problem 4 (b)

Internal problem ID [18253]
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 : 4 (b)
Date solved : Tuesday, January 28, 2025 at 11:44:23 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=6 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 22

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

\[ y(x)\to -3 x+\frac {1}{2} c_1 e^{2 x}+c_2 \]