50.14.8 problem 1(h)

Internal problem ID [8046]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 1(h)
Date solved : Monday, January 27, 2025 at 03:37:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

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

\[ y = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1} +\frac {{\mathrm e}^{3 x}}{8} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 29

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

\[ y(x)\to \frac {e^{3 x}}{8}+c_1 e^x+c_2 e^{-x} \]