89.3.3 problem 3

Internal problem ID [24301]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 34
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:12:40 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 49

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

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

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 53

ode=(2*x*y[x]-3*x^2)+( 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+2 x^3+c_1}\\ y(x)&\to -x^2+\sqrt {x^4+2 x^3+c_1} \end{align*}

✗ Sympy

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

Timed Out