50.14.25 problem 4(a)

Internal problem ID [8063]
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 : 4(a)
Date solved : Monday, January 27, 2025 at 03:41:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 25

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

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