Internal problem ID [5539]
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 2.1. Linear Equations with Constant
Coefficients. Page 62
Problem number: 2(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+8 y^{\prime }-9 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)+8*diff(y(x),x)-9*y(x)=0,y(1) = 2, D(y)(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {9 \,{\mathrm e}^{x -1}}{5}+\frac {{\mathrm e}^{9-9 x}}{5} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 26
DSolve[{y''[x]+8*y'[x]-9*y[x]==0,{y[1]==2,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} e^{9-9 x}+\frac {9 e^{x-1}}{5} \\ \end{align*}