53.1.819 problem 843

Internal problem ID [11291]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 843
Date solved : Tuesday, September 30, 2025 at 07:37:39 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

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

\[ y = c_1 x +c_2 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

ode=D[y[x],{x,2}]==((4*(1/2)^2-1)/(4*x^2))*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.015 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} + C_{2} x \]