44.2.44 problem 44

Internal problem ID [6976]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 44
Date solved : Sunday, March 30, 2025 at 11:32:36 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y^{\prime }\left (\frac {\pi }{2}\right )&=1\\ y^{\prime }\left (\pi \right )&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

{}

✗ Sympy

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

ValueError : Couldnt solve for initial conditions