60.3.9 problem 1009

Internal problem ID [11019]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1009
Date solved : Monday, January 27, 2025 at 10:41:56 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(diff(diff(y(x),x),x)+l*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 28

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

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