84.6.3 problem 3.‘0

Internal problem ID [22104]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Supplementary problems
Problem number : 3.‘0
Date solved : Thursday, October 02, 2025 at 08:24:56 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 51

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

\begin{align*} y &= \left (x^{3}+c_1 \right )^{{1}/{3}} \\ y &= -\frac {\left (x^{3}+c_1 \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2} \\ y &= \frac {\left (x^{3}+c_1 \right )^{{1}/{3}} \left (-1+i \sqrt {3}\right )}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 62

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

\begin{align*} y(x)&\to \sqrt [3]{x^3+3 c_1}\\ y(x)&\to -\sqrt [3]{-1} \sqrt [3]{x^3+3 c_1}\\ y(x)&\to (-1)^{2/3} \sqrt [3]{x^3+3 c_1} \end{align*}

✓ Sympy. Time used: 0.408 (sec). Leaf size: 53

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

\[ \left [ y{\left (x \right )} = \sqrt [3]{C_{1} + x^{3}}, \ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \sqrt [3]{C_{1} + x^{3}}}{2}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \sqrt [3]{C_{1} + x^{3}}}{2}\right ] \]