83.37.6 problem 6

Internal problem ID [19372]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (B) at page 128
Problem number : 6
Date solved : Thursday, March 13, 2025 at 02:22:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y&=0 \end{align*}

✗ Maple

ode:=4*x^2*diff(diff(y(x),x),x)+4*x^5*diff(y(x),x)+(x^3+6*x^2+4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=4*x^2*D[y[x],{x,2}]+4*x^5*D[y[x],x]+(x^3+6*x^2+4)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**5*Derivative(y(x), x) + 4*x**2*Derivative(y(x), (x, 2)) + (x**3 + 6*x**2 + 4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None