83.2.2 problem 1 (b)

Internal problem ID [21913]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. III at page 35
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 08:09:24 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 57

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

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

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 96

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

\begin{align*} y(x)&\to -\sqrt [4]{2} \sqrt [4]{x^3+2 c_1}\\ y(x)&\to -i \sqrt [4]{2} \sqrt [4]{x^3+2 c_1}\\ y(x)&\to i \sqrt [4]{2} \sqrt [4]{x^3+2 c_1}\\ y(x)&\to \sqrt [4]{2} \sqrt [4]{x^3+2 c_1} \end{align*}

✓ Sympy. Time used: 0.744 (sec). Leaf size: 54

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

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{C_{1} + 2 x^{3}}, \ y{\left (x \right )} = i \sqrt [4]{C_{1} + 2 x^{3}}, \ y{\left (x \right )} = - \sqrt [4]{C_{1} + 2 x^{3}}, \ y{\left (x \right )} = \sqrt [4]{C_{1} + 2 x^{3}}\right ] \]