89.9.13 problem 14

Internal problem ID [24493]
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 : 14
Date solved : Thursday, October 02, 2025 at 10:42:40 PM
CAS classification : [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 68

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

\begin{align*} y &= \frac {-{\mathrm e}^{-\frac {x^{2}}{2}} \sqrt {x^{2} {\mathrm e}^{x^{2}} c_1^{2}+1}+c_1 x}{c_1} \\ y &= \frac {{\mathrm e}^{-\frac {x^{2}}{2}} \sqrt {x^{2} {\mathrm e}^{x^{2}} c_1^{2}+1}+c_1 x}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 40.721 (sec). Leaf size: 145

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

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

✗ Sympy

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

Timed Out