59.1.156 problem 158

Internal problem ID [9328]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 158
Date solved : Sunday, March 30, 2025 at 02:32:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (1+x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 19

ode:=4*x^2*(1+x)*diff(diff(y(x),x),x)+8*x^2*diff(y(x),x)+(1+x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {x}\, \left (\ln \left (x \right ) c_2 +c_1 \right )}{1+x} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 24

ode=4*x^2*(1+x)*D[y[x],{x,2}]+8*x^2*D[y[x],x]+(1+x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\sqrt {x} (c_2 \log (x)+c_1)}{x+1} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*(x + 1)*Derivative(y(x), (x, 2)) + 8*x**2*Derivative(y(x), x) + (x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False