29.9.4 problem 2, using elementary method

Internal problem ID [7374]
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 elementary 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*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(y(x),x) = 3*x^2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{x^{3}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 18

ode=D[y[x],x]==3*x^2*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{x^3}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 8

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)
 

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