43.21.1 problem 1(a)

Internal problem ID [9017]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 1(a)
Date solved : Tuesday, September 30, 2025 at 06:01:27 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.149 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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