86.6.2 problem 2

Internal problem ID [23135]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5b at page 77
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:23:17 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y \left (\frac {\pi \sqrt {3}}{6}\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)+3*y(x) = 0; 
ic:=[y(0) = 0, y(1/6*3^(1/2)*Pi) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 4 \sin \left (\sqrt {3}\, x \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 15

ode=D[y[x],{x,2}]+3*y[x]==0; 
ic={y[0]==0,y[Pi/(2*Sqrt[3])]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 \sin \left (\sqrt {3} x\right ) \end{align*}

✓ Sympy. Time used: 0.034 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 5, y(sqrt(3)*pi/6): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 4 \sin {\left (\sqrt {3} x \right )} + 5 \cos {\left (\sqrt {3} x \right )} \]