88.24.3 problem 3

Internal problem ID [24196]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 7. Series Methods. Exercises at page 202
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:00:44 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 22

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

\[ y(x)\to c_1 \left (\frac {3 x^4}{8}-\frac {3 x^2}{2}+1\right ) \]

✓ Sympy. Time used: 0.209 (sec). Leaf size: 24

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

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