49.4.2 problem 1(b)

Internal problem ID [7613]
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 : Monday, January 27, 2025 at 03:07:33 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(3*diff(y(x),x$2)+2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 32

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

\[ y(x)\to c_1 \cos \left (\sqrt {\frac {2}{3}} x\right )+c_2 \sin \left (\sqrt {\frac {2}{3}} x\right ) \]