58.2.35 problem 35

Internal problem ID [9158]
Book : Second order enumerated odes
Section : section 2
Problem number : 35
Date solved : Sunday, March 30, 2025 at 02:24:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 33

ode:=4*x^2*diff(diff(y(x),x),x)+4*x^5*diff(y(x),x)+(x^8+6*x^4+4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x^{4}}{8}} \sqrt {x}\, \left (x^{-\frac {i \sqrt {3}}{2}} c_2 +x^{\frac {i \sqrt {3}}{2}} c_1 \right ) \]

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 62

ode=4*x^2*D[y[x],{x,2}]+4*x^5*D[y[x],x]+(x^8+6*x^4+4)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} e^{-\frac {x^4}{8}} x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}} \left (3 c_1-i \sqrt {3} c_2 x^{i \sqrt {3}}\right ) \]

✗ 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**8 + 6*x**4 + 4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None