70.13.10 problem 10

Internal problem ID [18879]
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 : 10
Date solved : Thursday, October 02, 2025 at 03:32:26 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=9*diff(diff(y(x),x),x)+12*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 20

ode=9*D[y[x],{x,2}]+12*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x/3} (c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + 12*Derivative(y(x), x) + 9*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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