7.8.4 problem 4

Internal problem ID [218]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 4
Date solved : Wednesday, February 05, 2025 at 03:18:11 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+25 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=10\\ y^{\prime }\left (0\right )&=-10 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+25*y(x)=0,y(0) = 10, D(y)(0) = -10],y(x), singsol=all)
 

\[ y = -2 \sin \left (5 x \right )+10 \cos \left (5 x \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]+25*y[x] == 0,{y[0]==10,Derivative[1][y][0] ==-10}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 10 \cos (5 x)-2 \sin (5 x) \]