84.12.1 problem 6.6

Internal problem ID [22143]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 6. Exact first-order differential equations. Supplementary problems
Problem number : 6.6
Date solved : Thursday, October 02, 2025 at 08:32:21 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

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

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

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 60

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

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

✓ Sympy. Time used: 0.567 (sec). Leaf size: 36

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

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