44.2.42 problem 42

Internal problem ID [6974]
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 : 42
Date solved : Monday, January 27, 2025 at 02:39:24 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (\pi \right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)+4*y(x)=0,y(0) = 1, D(y)(Pi) = 5],y(x), singsol=all)
 

\[ y = \frac {5 \sin \left (2 x \right )}{2}+\cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 16

DSolve[{D[y[x],{x,2}]+4*y[x]==0,{y[0] == 1,Derivative[1][y][Pi] == 5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (2 x)+5 \sin (x) \cos (x) \]