85.7.5 problem 1 (e)

Internal problem ID [22459]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 32
Problem number : 1 (e)
Date solved : Thursday, October 02, 2025 at 08:39:50 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x -2 y}{y-2 x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.391 (sec). Leaf size: 114

ode:=diff(y(x),x) = (x-2*y(x))/(y(x)-2*x); 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\begin{align*} y &= \frac {3 \left (-x +\sqrt {x^{2}-1}\right )^{{2}/{3}}+3}{\left (-x +\sqrt {x^{2}-1}\right )^{{1}/{3}}}-x \\ y &= \frac {-3 i \sqrt {3}\, \left (-x +\sqrt {x^{2}-1}\right )^{{2}/{3}}+3 i \sqrt {3}-3 \left (-x +\sqrt {x^{2}-1}\right )^{{2}/{3}}-2 x \left (-x +\sqrt {x^{2}-1}\right )^{{1}/{3}}-3}{2 \left (-x +\sqrt {x^{2}-1}\right )^{{1}/{3}}} \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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