Internal problem ID [6321]
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]]
\[ \boxed {2 y^{\prime \prime }+3 y^{\prime }+y={\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -2 c_{1} {\mathrm e}^{-x}+\frac {{\mathrm e}^{-3 x}}{10}+{\mathrm e}^{-\frac {x}{2}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 45
DSolve[y''[x]+3*y'[x]+y[x]==Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x}+c_1 e^{-\frac {1}{2} \left (3+\sqrt {5}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {5}-3\right ) x} \]