Internal problem ID [2740]
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]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-6 y=18 \,{\mathrm e}^{5 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+diff(y(x),x)-6*y(x)=18*exp(5*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (3 \,{\mathrm e}^{8 x}+4 c_{1} {\mathrm e}^{5 x}+4 c_{2} \right ) {\mathrm e}^{-3 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 31
DSolve[y''[x]+y'[x]-6*y[x]==18*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 e^{5 x}}{4}+c_1 e^{-3 x}+c_2 e^{2 x} \]