87.24.7 problem 7

Internal problem ID [23789]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 5. Series solutions of second order linear equations. Exercise at page 218
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:45:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 93

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

\[ y(x)\to c_1 \left (\frac {31 x^5}{405}+\frac {17 x^4}{216}+\frac {2 x^3}{27}+\frac {x^2}{6}+1\right )+c_2 e^{\frac {2}{x}-\frac {3}{2 x^2}} \left (-\frac {506 x^5}{405}+\frac {239 x^4}{54}-\frac {4 x^3}{3}+\frac {4 x^2}{9}-\frac {4 x}{3}+1\right ) x^6 \]

✗ Sympy

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

ValueError : ODE x**3*(1 - x**2)*Derivative(y(x), (x, 2)) + x*y(x) + (2*x - 3)*Derivative(y(x), x) d