84.3.7 problem 2.7

Internal problem ID [22084]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 2. Solutions. Solved problems page 5
Problem number : 2.7
Date solved : Thursday, October 02, 2025 at 08:23:41 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{8}\right )&=0 \\ y \left (\frac {\pi }{6}\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=[y(1/8*Pi) = 0, y(1/6*Pi) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 27

ode=D[y[x],{x,2}]+4*y[x]==0; 
ic={y[Pi/8]==0,y[Pi/6] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {2 (\cos (2 x)-\sin (2 x))}{\sqrt {3}-1} \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(pi/8): 0, y(pi/6): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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