47.2.33 problem 31

Internal problem ID [7449]
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 : 31
Date solved : Sunday, March 30, 2025 at 12:07:13 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.236 (sec). Leaf size: 115

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

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

✓ Mathematica. Time used: 60.183 (sec). Leaf size: 1601

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

Too large to display

✗ Sympy

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

Timed Out