81.7.3 problem 4

Internal problem ID [18700]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 12:10:45 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=-a^{2} y \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)=-a^2*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} \sin \left (a x \right )+c_{2} \cos \left (a x \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]==-a^2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

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