Internal problem ID [605]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-9 y^{\prime }+9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 27
dsolve(diff(y(x),x$2) -9*diff(y(x),x)+9*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {3 \left (3+\sqrt {5}\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {3 \left (\sqrt {5}-3\right ) x}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 36
DSolve[y''[x]-9*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {3}{2} \left (\sqrt {5}-3\right ) x} \left (c_2 e^{3 \sqrt {5} x}+c_1\right ) \\ \end{align*}