59.1.511 problem 527

Internal problem ID [9683]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 527
Date solved : Sunday, March 30, 2025 at 02:44:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.047 (sec). Leaf size: 36

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

\[ y = \frac {c_1 \,x^{{4}/{3}} \left (x^{2}+20 x +70\right )+c_2 \operatorname {hypergeom}\left (\left [3\right ], \left [-\frac {1}{3}\right ], \frac {x}{3}\right ) {\mathrm e}^{-\frac {x}{3}}}{x^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.357 (sec). Leaf size: 60

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

\[ y(x)\to e x \left (x^2+20 x+70\right ) \left (c_2 \int _1^x\frac {e^{-\frac {K[1]}{3}-\frac {7}{3}}}{K[1]^{7/3} \left (K[1]^2+20 K[1]+70\right )^2}dK[1]+c_1\right ) \]

✗ Sympy

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

False