59.1.127 problem 129

Internal problem ID [9299]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 129
Date solved : Sunday, March 30, 2025 at 02:31:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.086 (sec). Leaf size: 32

ode:=9*x^2*diff(diff(y(x),x),x)+3*x*(-2*x^2+3*x+5)*diff(y(x),x)+(-14*x^2+12*x+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\frac {x \left (x -3\right )}{3}} \left (\int \frac {{\mathrm e}^{-\frac {x \left (x -3\right )}{3}}}{x}d x c_2 +c_1 \right )}{x^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.476 (sec). Leaf size: 52

ode=9*x^2*D[y[x],{x,2}]+3*x*(5+3*x-2*x^2)*D[y[x],x]+(1+12*x-14*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*Derivative(y(x), (x, 2)) + 3*x*(-2*x**2 + 3*x + 5)*Derivative(y(x), x) + (-14*x**2 + 12*x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False