50.11.5 problem 1(e)

Internal problem ID [7989]
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 2.3. THE METHOD OF VARIATION OF PARAMETERS. Page 71
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:35:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

\[ y = \frac {{\mathrm e}^{-3 x}}{10}-2 c_{1} {\mathrm e}^{-x}+{\mathrm e}^{-\frac {x}{2}} c_{2} \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 45

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

\[ y(x)\to e^{-3 x}+c_1 e^{-\frac {1}{2} \left (3+\sqrt {5}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {5}-3\right ) x} \]