73.8.13 problem 13.2 (g)

Internal problem ID [15221]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.2 (g)
Date solved : Tuesday, January 28, 2025 at 07:50:17 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

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

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