59.1.157 problem 159

Internal problem ID [9329]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 159
Date solved : Wednesday, March 05, 2025 at 07:47:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} \left (3+x \right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 19

ode:=9*x^2*(x+3)*diff(diff(y(x),x),x)+3*x*(3+7*x)*diff(y(x),x)+(3+4*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.303 (sec). Leaf size: 49

ode=9*x^2*(3+x)*D[y[x],{x,2}]+3*x*(3+7*x)*D[y[x],x]+(3+4*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*(x + 3)*Derivative(y(x), (x, 2)) + 3*x*(7*x + 3)*Derivative(y(x), x) + (4*x + 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False