7.5.45 problem 45

Internal problem ID [149]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 45
Date solved : Friday, February 07, 2025 at 07:58:41 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \sin \left (2 x \right )+c_2 \cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 20

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

\[ y(x)\to c_1 \cos (2 x)+c_2 \sin (2 x) \]