26.7.11 problem Exercise 20.12, page 220

Internal problem ID [7061]
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 : Tuesday, September 30, 2025 at 04:21:03 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to e^{-6 k x} \left (c_2 e^{8 k x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
k = symbols("k") 
y = Function("y") 
ode = Eq(-12*k**2*y(x) + 4*k*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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