10.7.7 problem 7

Internal problem ID [1255]
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
Date solved : Monday, January 27, 2025 at 04:48:00 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+9 y&=0 \end{align*}

✓ 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)
 

\[ y = c_1 \,{\mathrm e}^{\frac {3 \left (3+\sqrt {5}\right ) x}{2}}+c_2 \,{\mathrm e}^{-\frac {3 \left (\sqrt {5}-3\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]-9*D[y[x],x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {3}{2} \left (\sqrt {5}-3\right ) x} \left (c_2 e^{3 \sqrt {5} x}+c_1\right ) \]