56.4.59 problem 56

Internal problem ID [8948]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 56
Date solved : Sunday, March 30, 2025 at 01:56:09 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 32

Order:=6; 
ode:=2*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \frac {x^{-\frac {i \sqrt {23}}{4}} c_1 +x^{\frac {i \sqrt {23}}{4}} c_2}{x^{{3}/{4}}}+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 44

ode=2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 x^{\frac {1}{4} \left (-3+i \sqrt {23}\right )}+c_2 x^{\frac {1}{4} \left (-3-i \sqrt {23}\right )} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : Expected Expr or iterable but got None