59.1.119 problem 121

Internal problem ID [9291]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 121
Date solved : Sunday, March 30, 2025 at 02:31:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} \left (1+x \right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 19

ode:=3*x^2*(1+x)^2*diff(diff(y(x),x),x)-x*(-11*x^2-10*x+1)*diff(y(x),x)+(5*x^2+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.242 (sec). Leaf size: 58

ode=3*x^2*(1+x)^2*D[y[x],{x,2}]-x*(1-10*x-11*x^2)*D[y[x],x]+(1+5*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \sqrt [6]{x} \left (3 c_2 x^{2/3}+2 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {4}{K[1]+1}-\frac {1}{3 K[1]}\right )dK[1]\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*(x + 1)**2*Derivative(y(x), (x, 2)) - x*(-11*x**2 - 10*x + 1)*Derivative(y(x), x) + (5*x**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False