78.1.15 problem 2.e

Internal problem ID [20941]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 2.e
Date solved : Thursday, October 02, 2025 at 06:49:47 PM
CAS classification : [_rational]

\begin{align*} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 65

ode:=2*x*y(x)^2-3*y(x)^3+(7-3*x*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {x^{2}+c_1 +\sqrt {x^{4}+2 c_1 \,x^{2}+c_1^{2}-84 x}}{6 x} \\ y &= \frac {x^{2}-\sqrt {x^{4}+2 c_1 \,x^{2}+c_1^{2}-84 x}+c_1}{6 x} \\ \end{align*}

✓ Mathematica. Time used: 0.263 (sec). Leaf size: 86

ode=(2*x*y[x]^2-3*y[x]^3)+(7-3*x*y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2-\sqrt {x^4+2 c_1 x^2-84 x+c_1{}^2}+c_1}{6 x}\\ y(x)&\to \frac {x^2+\sqrt {x^4+2 c_1 x^2-84 x+c_1{}^2}+c_1}{6 x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 1.820 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**2 + (-3*x*y(x)**2 + 7)*Derivative(y(x), x) - 3*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + 2 x^{2} - \sqrt {C_{1}^{2} + 4 C_{1} x^{2} + 4 x^{4} - 336 x}}{12 x} \]