54.3.362 problem 1379

Internal problem ID [12657]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1379
Date solved : Wednesday, October 01, 2025 at 02:19:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {12 y}{\left (x +1\right )^{2} \left (x^{2}+2 x +3\right )} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 60

ode:=diff(diff(y(x),x),x) = 12/(1+x)^2/(x^2+2*x+3)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3 \left (x^{2}+2 x +3\right ) c_2 \arctan \left (\frac {\left (x +1\right ) \sqrt {2}}{2}\right )-c_2 \left (x^{3}+2 x^{2}+4 x +1\right ) \sqrt {2}+c_1 \left (x^{2}+2 x +3\right )}{\left (x +1\right )^{2}} \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 80

ode=D[y[x],{x,2}] == (12*y[x])/((1 + x)^2*(3 + 2*x + x^2)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x-\frac {4}{K[1]^3+3 K[1]^2+5 K[1]+3}dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}-\frac {4}{K[1]^3+3 K[1]^2+5 K[1]+3}dK[1]\right )dK[2]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - 12*y(x)/((x + 1)**2*(x**2 + 2*x + 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), (x, 2)) - 12*y(x)/((x + 1)**2*(x**2 + 2*x + 3)) cannot be solved by the hypergeometric method