87.15.15 problem 15

Internal problem ID [23563]
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 2. Linear differential equations. Exercise at page 115
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:42:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+2\right ) 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: 0.004 (sec). Leaf size: 34

Order:=6; 
ode:=(x^2+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);
 

\[ y = \left (-x^{2}+1\right ) y \left (0\right )+\left (x -\frac {1}{12} x^{3}+\frac {1}{480} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 33

ode=(x^2+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}]
 

\[ y(x)\to c_1 \left (1-x^2\right )+c_2 \left (\frac {x^5}{480}-\frac {x^3}{12}+x\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 + 2)*Derivative(y(x), (x, 2)) + 4*y(x) - 3*xDerivative(y(x), (x, 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

TypeError : cannot unpack non-iterable Dummy object