54.3.9 problem 1009

Internal problem ID [12304]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1009
Date solved : Wednesday, October 01, 2025 at 01:42:58 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to c_1 \cos \left (\sqrt {l} x\right )+c_2 \sin \left (\sqrt {l} x\right ) \end{align*}

✓ Sympy. Time used: 0.043 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
l = symbols("l") 
y = Function("y") 
ode = Eq(l*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x \sqrt {- l}} + C_{2} e^{x \sqrt {- l}} \]