44.2.41 problem 41

Internal problem ID [6973]
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 : 41
Date solved : Monday, January 27, 2025 at 02:39:22 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 5

dsolve([diff(y(x),x$2)+4*y(x)=0,D(y)(0) = 0, D(y)(1/6*Pi) = 0],y(x), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]