71.10.11 problem 11

Internal problem ID [14506]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 06:42:44 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)+alpha*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 28

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

\[ y(x)\to c_1 \cos \left (\sqrt {a} x\right )+c_2 \sin \left (\sqrt {a} x\right ) \]