84.34.10 problem 20.23 (b)

Internal problem ID [22337]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 20. Regular singular points and the method of Frobenius. Supplementary problems
Problem number : 20.23 (b)
Date solved : Thursday, October 02, 2025 at 08:37:43 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 19

Order:=6; 
ode:=x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = x^{2} \left (c_1 +c_2 \ln \left (x \right )\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}]-(3*x)*D[y[x],x]+4*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 x^2+c_2 x^2 \log (x) \]

✓ Sympy. Time used: 0.194 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 3*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)
 

\[ y{\left (x \right )} = C_{1} x^{2} + O\left (x^{6}\right ) \]