59.1.180 problem 182

Internal problem ID [9352]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 182
Date solved : Sunday, March 30, 2025 at 02:33:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 45

ode:=x^2*(1+x)*diff(diff(y(x),x),x)-x*(6+11*x)*diff(y(x),x)+(6+32*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 3 c_1 \,x^{8}+14 c_1 \,x^{7}+21 c_1 \,x^{6}+35 c_2 \,x^{4}+42 c_2 \,x^{3}+21 c_2 \,x^{2}+4 c_2 x \]

✓ Mathematica. Time used: 0.528 (sec). Leaf size: 122

ode=x^2*(1+x)*D[y[x],{x,2}]-x*(6+11*x)*D[y[x],x]+(6+32*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} (3 x-4) \exp \left (\int _1^x\left (\frac {7}{2 (K[1]+1)}-\frac {2}{K[1]}\right )dK[1]-\frac {1}{2} \int _1^x\left (-\frac {5}{K[2]+1}-\frac {6}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\frac {9 \exp \left (-2 \int _1^{K[3]}\frac {3 K[1]-4}{2 K[1] (K[1]+1)}dK[1]\right )}{(4-3 K[3])^2}dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x + 1)*Derivative(y(x), (x, 2)) - x*(11*x + 6)*Derivative(y(x), x) + (32*x + 6)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None