90.12.10 problem 10

Internal problem ID [25212]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 213
Problem number : 10
Date solved : Thursday, October 02, 2025 at 11:59:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-12 y^{\prime }+18 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=2*diff(diff(y(t),t),t)-12*diff(y(t),t)+18*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{3 t} \left (c_2 t +c_1 \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 34

ode=D[y[t],{t,2}]-12*D[y[t],t]+18*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-3 \left (\sqrt {2}-2\right ) t} \left (c_2 e^{6 \sqrt {2} t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(18*y(t) - 12*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{3 t \left (2 - \sqrt {2}\right )} + C_{2} e^{3 t \left (\sqrt {2} + 2\right )} \]