80.3.27 problem 28

Internal problem ID [21191]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 28
Date solved : Thursday, October 02, 2025 at 07:16:38 PM
CAS classification : [_separable]

\begin{align*} x -2 y^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

ode:=x-2*diff(y(x),x)*y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 75

ode=x-2*y[x]^3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt [4]{x^2+4 c_1}\\ y(x)&\to -i \sqrt [4]{x^2+4 c_1}\\ y(x)&\to i \sqrt [4]{x^2+4 c_1}\\ y(x)&\to \sqrt [4]{x^2+4 c_1} \end{align*}

✓ Sympy. Time used: 0.687 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - 2*y(x)**3*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{C_{1} + x^{2}}, \ y{\left (x \right )} = i \sqrt [4]{C_{1} + x^{2}}, \ y{\left (x \right )} = - \sqrt [4]{C_{1} + x^{2}}, \ y{\left (x \right )} = \sqrt [4]{C_{1} + x^{2}}\right ] \]