60.3.370 problem 1387

Internal problem ID [11366]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1387
Date solved : Sunday, March 30, 2025 at 08:18:28 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }&=\frac {3 y}{4 \left (x^{2}+x +1\right )^{2}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x) = 3/4/(x^2+x+1)^2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sqrt {x^{2}+x +1}\, \left (\arctan \left (\frac {\left (2 x +1\right ) \sqrt {3}}{3}\right ) c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 0.193 (sec). Leaf size: 39

ode=D[y[x],{x,2}] == (3*y[x])/(4*(1 + x + x^2)^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {x^2+x+1} \left (c_2 \int _1^x\frac {1}{K[1]^2+K[1]+1}dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - 3*y(x)/(4*(x**2 + x + 1)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

IndexError : list index out of range