89.9.2 problem 2

Internal problem ID [24482]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 72
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:42:06 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 59

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

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

✓ Mathematica. Time used: 15.851 (sec). Leaf size: 88

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

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

✗ Sympy

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

Timed Out