8.7.3 problem 3

Internal problem ID [809]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 3
Date solved : Wednesday, February 05, 2025 at 04:29:37 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 )&=3\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+4*y(x)=0,y(0) = 3, D(y)(0) = 8],y(x), singsol=all)
 

\[ y = 4 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]+4*y[x]==0,{y[0]==3,Derivative[1][y][0] ==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 4 \sin (2 x)+3 \cos (2 x) \]