59.1.97 problem 99

Internal problem ID [9269]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 99
Date solved : Wednesday, March 05, 2025 at 07:46:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 19

ode:=2*x^2*(3*x+2)*diff(diff(y(x),x),x)+x*(4+11*x)*diff(y(x),x)-(1-x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{2} \left (2+3 x \right )^{{1}/{6}}+c_{1}}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.323 (sec). Leaf size: 69

ode=2*x^2*(2+3*x)*D[y[x],{x,2}]+x*(4+11*x)*D[y[x],x]-(1-x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt [6]{2} (3 x+2)^{5/12} \left (c_2 \sqrt [6]{3 x+2}+2^{2/3} c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {5}{6 K[1]+4}+\frac {1}{K[1]}\right )dK[1]\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*(3*x + 2)*Derivative(y(x), (x, 2)) + x*(11*x + 4)*Derivative(y(x), x) - (1 - x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False