Internal problem ID [10082]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2 Equations Containing Power
Functions. page 213
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\sqrt {a}\, x \right )+c_{2} \cos \left (\sqrt {a}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 28
DSolve[y''[x]+a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos \left (\sqrt {a} x\right )+c_2 \sin \left (\sqrt {a} x\right ) \\ \end{align*}