Internal problem ID [5568]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+3 y^{\prime }+y-{\mathrm e}^{-3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (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)
\[ y \relax (x ) = -2 \,{\mathrm e}^{-x} c_{1}+\frac {{\mathrm e}^{-3 x}}{10}+{\mathrm e}^{-\frac {x}{2}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 45
DSolve[y''[x]+3*y'[x]+y[x]==Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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} \\ \end{align*}