86.1.1 problem 1

Internal problem ID [23063]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3b at page 43
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:18:29 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

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

\begin{align*} y &= -\frac {\sqrt {6 x^{3}+9 c_1}}{3} \\ y &= \frac {\sqrt {6 x^{3}+9 c_1}}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to -\sqrt {\frac {2}{3}} \sqrt {x^3+3 c_1}\\ y(x)&\to \sqrt {\frac {2}{3}} \sqrt {x^3+3 c_1} \end{align*}

✓ Sympy. Time used: 0.209 (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)
 

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