32.7.11 problem Exercise 20.12, page 220

Internal problem ID [5926]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.12, page 220
Date solved : Monday, January 27, 2025 at 01:27:37 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+4*k*diff(y(x),x)-12*k^2*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{8 k x}+c_{2} \right ) {\mathrm e}^{-6 k x} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]+4*k*D[y[x],x]-12*k^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-6 k x} \left (c_2 e^{8 k x}+c_1\right ) \]