73.6.5 problem 7.4 (c)

Internal problem ID [15065]
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 (c)
Date solved : Thursday, March 13, 2025 at 05:34:41 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 58

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

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

✓ Mathematica. Time used: 0.187 (sec). Leaf size: 71

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

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

✓ Sympy. Time used: 1.218 (sec). Leaf size: 63

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

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