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 : Monday, January 27, 2025 at 02:39:30 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 (\frac {\pi }{2}\right )&=1\\ y^{\prime }\left (\pi \right )&=0 \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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