28.1.21 problem 21

Internal problem ID [4327]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 21
Date solved : Sunday, March 30, 2025 at 03:01:31 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 53

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

\begin{align*} y &= \frac {-6-\sqrt {12 x^{3}+18 c_1 +54 x +36}}{3 x} \\ y &= \frac {-6+\sqrt {12 x^{3}+18 c_1 +54 x +36}}{3 x} \\ \end{align*}

✓ Mathematica. Time used: 0.784 (sec). Leaf size: 87

ode=(2*x^2-x*y[x]^2-2*y[x]+3)-(x^2*y[x]+2*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {6 x+\sqrt {3} \sqrt {x^2 \left (4 x^3+18 x+12+3 c_1\right )}}{3 x^2} \\ y(x)\to \frac {-6 x+\sqrt {3} \sqrt {x^2 \left (4 x^3+18 x+12+3 c_1\right )}}{3 x^2} \\ \end{align*}

✗ Sympy

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

Timed Out