10.8.11 problem 17

Internal problem ID [1283]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
Problem number : 17
Date solved : Monday, January 27, 2025 at 04:49:39 AM
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 )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 10

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

\[ y(x)\to \sin (x) \cos (x) \]