Internal problem ID [5561]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y-{\mathrm e}^{2 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-3*y(x)=exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\sqrt {3}\, x} c_{2} +{\mathrm e}^{-\sqrt {3}\, x} c_{1} +{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 36
DSolve[y''[x]-3*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x}+c_1 e^{\sqrt {3} x}+c_2 e^{-\sqrt {3} x} \\ \end{align*}