29.9.3 problem 2, using series method

Internal problem ID [7373]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 2, using series method
Date solved : Tuesday, September 30, 2025 at 04:30:00 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x^{2} y \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

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

\[ y = \left (x^{3}+1\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 11

ode=D[y[x],x]==3*x^2*y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (x^3+1\right ) \]

✓ Sympy. Time used: 0.151 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} + C_{1} x^{3} + O\left (x^{6}\right ) \]