88.8.10 problem 10

Internal problem ID [24018]
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 44
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:54:16 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.154 (sec). Leaf size: 55

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

\[ y = \frac {-6 c_1 \operatorname {RootOf}\left (6 c_1 \,\textit {\_Z}^{10}-5 x^{2} \textit {\_Z}^{8}+c_1 \right )^{8}+5 x^{2} \operatorname {RootOf}\left (6 c_1 \,\textit {\_Z}^{10}-5 x^{2} \textit {\_Z}^{8}+c_1 \right )^{6}}{c_1^{2}} \]

✓ Mathematica. Time used: 2.04 (sec). Leaf size: 126

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

\begin{align*} y(x)&\to \text {Root}\left [10 \text {$\#$1}^5 c_1+5 \text {$\#$1} x^2-6\&,1\right ]\\ y(x)&\to \text {Root}\left [10 \text {$\#$1}^5 c_1+5 \text {$\#$1} x^2-6\&,2\right ]\\ y(x)&\to \text {Root}\left [10 \text {$\#$1}^5 c_1+5 \text {$\#$1} x^2-6\&,3\right ]\\ y(x)&\to \text {Root}\left [10 \text {$\#$1}^5 c_1+5 \text {$\#$1} x^2-6\&,4\right ]\\ y(x)&\to \text {Root}\left [10 \text {$\#$1}^5 c_1+5 \text {$\#$1} x^2-6\&,5\right ]\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.279 (sec). Leaf size: 27

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

\[ - \log {\left (x \right )} + \frac {\log {\left (x^{2} y{\left (x \right )} \right )}}{2} - \frac {\log {\left (x^{2} y{\left (x \right )} - \frac {6}{5} \right )}}{10} = C_{1} \]