81.1.27 problem 2-25

Internal problem ID [21472]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-25
Date solved : Thursday, October 02, 2025 at 07:39:17 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (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: 0.016 (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: 0.157 (sec). Leaf size: 29

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)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} + 6 x^{3}}}{3}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} + 6 x^{3}}}{3}\right ] \]