83.14.2 problem 2 (a)

Internal problem ID [22017]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter X. Solution in power series. Ex. XVIII at page 174
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 08:21:42 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (2 x -1\right ) y^{\prime \prime }-3 y^{\prime }&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

Order:=6; 
ode:=(2*x-1)*diff(diff(y(x),x),x)-3*diff(y(x),x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = y \left (0\right )+\left (x -\frac {3}{2} x^{2}+\frac {1}{2} x^{3}+\frac {1}{8} x^{4}+\frac {3}{40} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 39

ode=(2*x-1)*D[y[x],{x,2}]-3*D[y[x],x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (\frac {3 x^5}{40}+\frac {x^4}{8}+\frac {x^3}{2}-\frac {3 x^2}{2}+x\right )+c_1 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x - 1)*Derivative(y(x), (x, 2)) - 3*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

IndexError : list index out of range