73.6.4 problem 7.4 (b)

Internal problem ID [15072]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.4 (b)
Date solved : Monday, March 31, 2025 at 01:21:14 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 71

ode:=2*x*y(x)^3+4*x^3+3*x^2*y(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.206 (sec). Leaf size: 78

ode=2*x*y[x]^3+4*x^3+3*x^2*y[x]^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {\sqrt [3]{-x^4+c_1}}{x^{2/3}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-x^4+c_1}}{x^{2/3}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-x^4+c_1}}{x^{2/3}} \\ \end{align*}

✓ Sympy. Time used: 1.346 (sec). Leaf size: 63

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3 + 3*x**2*y(x)**2*Derivative(y(x), x) + 2*x*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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