59.1.179 problem 181

Internal problem ID [9351]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 181
Date solved : Sunday, March 30, 2025 at 02:32:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+2 x \right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 62

ode:=x^2*(2*x+1)*diff(diff(y(x),x),x)-2*x*(3+14*x)*diff(y(x),x)+(6+100*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 8 c_2 \,x^{10}+36 c_2 \,x^{9}+72 c_2 \,x^{8}+84 c_2 \,x^{7}+63 c_2 \,x^{6}+2016 c_1 \,x^{5}+672 c_1 \,x^{4}+144 c_1 \,x^{3}+18 c_1 \,x^{2}+c_1 x \]

✓ Mathematica. Time used: 0.282 (sec). Leaf size: 105

ode=x^2*(1+2*x)*D[y[x],{x,2}]-2*x*(3+14*x)*D[y[x],x]+(6+100*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {10}{2 K[1]+1}-\frac {2}{K[1]}\right )dK[1]-\frac {1}{2} \int _1^x-\frac {28 K[2]+6}{2 K[2]^2+K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\left (\frac {10}{2 K[1]+1}-\frac {2}{K[1]}\right )dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(2*x + 1)*Derivative(y(x), (x, 2)) - 2*x*(14*x + 3)*Derivative(y(x), x) + (100*x + 6)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None