88.26.10 problem 10

Internal problem ID [24230]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 7. Series Methods. Exercises at page 220
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:01:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 49

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

\[ y = c_1 \,x^{5} \left (1+\frac {1}{5} x +\operatorname {O}\left (x^{6}\right )\right )+c_2 x \left (\left (120 x^{4}+24 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \ln \left (x \right )+\left (-144+240 x -240 x^{2}+240 x^{3}-154 x^{4}-\frac {418}{5} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 56

ode=x^2*D[y[x],{x,2}]+(x^2-5*x)*D[y[x],{x,1}]+(5-6*x)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (\frac {x^6}{5}+x^5\right )+c_1 \left (\frac {1}{18} x \left (23 x^4-30 x^3+30 x^2-30 x+18\right )-\frac {5}{6} x^5 \log (x)\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + (5 - 6*x)*y(x) + (x**2 - 5*x)*Derivative(y(x), 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