88.12.20 problem 22

Internal problem ID [24076]
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. Miscellaneous Exercises at page 55
Problem number : 22
Date solved : Thursday, October 02, 2025 at 09:57:16 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 x y^{2}+\left (1-x^{2} y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.173 (sec). Leaf size: 43

ode:=2*x*y(x)^2+(1-x^2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.219 (sec). Leaf size: 66

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

\begin{align*} y(x)&\to -\frac {i}{\sqrt {-x^4-c_1}-i x^2}\\ y(x)&\to \frac {1}{x^2-i \sqrt {-x^4-c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.879 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**2 + (-x**2*y(x) + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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