Internal problem ID [5549]
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: 1(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 }+3 y^{\prime }-10 y-6 \,{\mathrm e}^{4 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+3*diff(y(x),x)-10*y(x)=6*exp(4*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-5 x} c_{2}+{\mathrm e}^{2 x} c_{1}+\frac {{\mathrm e}^{4 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 31
DSolve[y''[x]+3*y'[x]-10*y[x]==6*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{4 x}}{3}+c_1 e^{-5 x}+c_2 e^{2 x} \\ \end{align*}