Internal problem ID [2231]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear
Differential Equations. page 502
Problem number: Problem 38.
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^{\prime }-6 y-18 \,{\mathrm e}^{5 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+diff(y(x),x)-6*y(x)=18*exp(5*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{-3 x}+\frac {3 \,{\mathrm e}^{5 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 31
DSolve[y''[x]+y'[x]-6*y[x]==18*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 e^{5 x}}{4}+c_1 e^{-3 x}+c_2 e^{2 x} \\ \end{align*}