87.24.19 problem 19

Internal problem ID [23801]
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 : 19
Date solved : Thursday, October 02, 2025 at 09:45:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 198

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

\[ y(x)\to c_1 e^{-\frac {2}{\sqrt {x}}} x^{3/4} \left (-\frac {306822993137705 x^{9/2}}{4987384743591936}-\frac {5563931329 x^{7/2}}{270582939648}-\frac {369721 x^{5/2}}{25165824}-\frac {1045 x^{3/2}}{24576}+\frac {20925328131991481 x^5}{159596311794941952}+\frac {1140605922445 x^4}{34634616274944}+\frac {37341821 x^3}{2415919104}+\frac {30305 x^2}{1572864}+\frac {209 x}{512}+\frac {19 \sqrt {x}}{16}+1\right )+c_2 e^{\frac {2}{\sqrt {x}}} x^{3/4} \left (\frac {306822993137705 x^{9/2}}{4987384743591936}+\frac {5563931329 x^{7/2}}{270582939648}+\frac {369721 x^{5/2}}{25165824}+\frac {1045 x^{3/2}}{24576}+\frac {20925328131991481 x^5}{159596311794941952}+\frac {1140605922445 x^4}{34634616274944}+\frac {37341821 x^3}{2415919104}+\frac {30305 x^2}{1572864}+\frac {209 x}{512}-\frac {19 \sqrt {x}}{16}+1\right ) \]

✗ Sympy

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

ValueError : ODE x**3*Derivative(y(x), (x, 2)) - (x + 1)*y(x) does not match hint 2nd_power_series_r