47.2.42 problem 40

Internal problem ID [7458]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 40
Date solved : Sunday, March 30, 2025 at 12:07:54 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x -2 y+5}{y-2 x -4} \end{align*}

✓ Maple. Time used: 0.235 (sec). Leaf size: 115

ode:=diff(y(x),x) = (x-2*y(x)+5)/(y(x)-2*x-4); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\left (i \sqrt {3}-1\right ) \left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +1\right )^{2}-1}+27 \left (x +1\right ) c_1 \right )^{{2}/{3}}-3 i \sqrt {3}-3+6 \left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +1\right )^{2}-1}+27 c_1 x +27 c_1 \right )^{{1}/{3}} \left (x -1\right ) c_1}{6 \left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +1\right )^{2}-1}+27 \left (x +1\right ) c_1 \right )^{{1}/{3}} c_1} \]

✓ Mathematica. Time used: 60.196 (sec). Leaf size: 1601

ode=D[y[x],x]==(x-2*y[x]+5)/(y[x]-2*x-4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x - 2*y(x) + 5)/(-2*x + y(x) - 4),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out