50.10.14 problem 4(a)

Internal problem ID [7983]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number : 4(a)
Date solved : Monday, January 27, 2025 at 03:35:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 36

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

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