43.4.2 problem 1(b)

Internal problem ID [8899]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 52
Problem number : 1(b)
Date solved : Tuesday, September 30, 2025 at 05:59:51 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=3*diff(diff(y(x),x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (\frac {\sqrt {6}\, x}{3}\right )+c_2 \cos \left (\frac {\sqrt {6}\, x}{3}\right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 32

ode=3*D[y[x],{x,2}]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \cos \left (\sqrt {\frac {2}{3}} x\right )+c_2 \sin \left (\sqrt {\frac {2}{3}} x\right ) \end{align*}

✓ Sympy. Time used: 0.027 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) + 3*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (\frac {\sqrt {6} x}{3} \right )} + C_{2} \cos {\left (\frac {\sqrt {6} x}{3} \right )} \]