10.9.4 problem 4

Internal problem ID [1306]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 4
Date solved : Saturday, March 29, 2025 at 10:51:48 PM
CAS classification : [[_2nd_order, _missing_x]]

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

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

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 20

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

\[ y(x)\to e^{-3 x/2} (c_2 x+c_1) \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 14

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

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