Internal problem ID [5642]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 4(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-3 \,{\mathrm e}^{2 x}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{2 x} \end {align*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)-y(x)=3*exp(2*x),exp(2*x)],y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 25
DSolve[y''[x]-y[x]==3*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x}+c_1 e^x+c_2 e^{-x} \\ \end{align*}