84.7.1 problem 4.1

Internal problem ID [22107]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Solved problems. Page 14
Problem number : 4.1
Date solved : Thursday, October 02, 2025 at 08:25:05 PM
CAS classification : [_separable]

\begin{align*} x -y^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 65

ode:=x-y(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\left (12 x^{2}+8 c_1 \right )^{{1}/{3}}}{2} \\ y &= -\frac {\left (12 x^{2}+8 c_1 \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y &= \frac {\left (12 x^{2}+8 c_1 \right )^{{1}/{3}} \left (-1+i \sqrt {3}\right )}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 79

ode=x-y[x]^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.878 (sec). Leaf size: 63

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

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