58.2.43 problem 43

Internal problem ID [9166]
Book : Second order enumerated odes
Section : section 2
Problem number : 43
Date solved : Sunday, March 30, 2025 at 02:24:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +6\right ) y^{\prime }+10 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 62

Order:=6; 
ode:=x^2*diff(diff(y(x),x),x)-x*(x+6)*diff(y(x),x)+10*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = x^{2} \left (c_1 \,x^{3} \left (1+\frac {5}{4} x +\frac {3}{4} x^{2}+\frac {7}{24} x^{3}+\frac {1}{12} x^{4}+\frac {3}{160} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_2 \left (\left (24 x^{3}+30 x^{4}+18 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \ln \left (x \right )+\left (12-12 x +18 x^{2}+26 x^{3}+x^{4}-9 x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )\right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 84

ode=x^2*D[y[x],{x,2}]-x*(x+6)*D[y[x],x]+10*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (\frac {1}{2} x^5 (5 x+4) \log (x)-\frac {1}{4} x^2 \left (3 x^4-6 x^3-6 x^2+4 x-4\right )\right )+c_2 \left (\frac {x^9}{12}+\frac {7 x^8}{24}+\frac {3 x^7}{4}+\frac {5 x^6}{4}+x^5\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*(x + 6)*Derivative(y(x), x) + 10*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