76.13.19 problem 19

Internal problem ID [17601]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 10:45:03 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)
 

\[ y = c_{1} {\mathrm e}^{\frac {3 \left (\sqrt {5}+3\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {3 \left (\sqrt {5}-3\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 36

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

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