Internal problem ID [613]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant
Coefficients, page 144
Problem number: 15.
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) = 1, y^{\prime }\relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 19
dsolve([diff(y(x),x$2) +8*diff(y(x),x)-9*y(x) = 0,y(1) = 1, D(y)(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{9-9 x}}{10}+\frac {9 \,{\mathrm e}^{x -1}}{10} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[{y''[x]+8*y'[x]-9*y[x]==0,{y[1]==1,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{10} e^{9-9 x}+\frac {9 e^{x-1}}{10} \\ \end{align*}