88.7.11 problem 11

Internal problem ID [24006]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 41
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:53:41 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {x -\sqrt {-4 x^{3}+x^{2}-4 c_1}}{2 x} \\ y &= \frac {x +\sqrt {-4 x^{3}+x^{2}-4 c_1}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.353 (sec). Leaf size: 71

ode=( 3*x-2*y[x]+2*y[x]^2 )+( 2*x*y[x]-x  )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.757 (sec). Leaf size: 41

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

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