87.12.19 problem 20

Internal problem ID [23467]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 20
Date solved : Thursday, October 02, 2025 at 09:42:05 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 }{4}\right )&=1 \\ y^{\prime }\left (\frac {\pi }{4}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 8

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

\[ y = \sin \left (2 x \right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 9

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

\begin{align*} y(x)&\to \sin (2 x) \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = \sin {\left (2 x \right )} \]