66.1.20 problem Problem 28

Internal problem ID [13796]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 28
Date solved : Monday, March 31, 2025 at 08:12:28 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.227 (sec). Leaf size: 115

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

\[ y = \frac {\frac {1}{2}+\frac {\left (1-i \sqrt {3}\right ) \left (27 \left (x +2\right ) c_1 +3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +2\right )^{2}-1}\right )^{{2}/{3}}}{6}+\frac {i \sqrt {3}}{2}-\left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +2\right )^{2}-1}+27 c_1 x +54 c_1 \right )^{{1}/{3}} \left (x +1\right ) c_1}{\left (27 \left (x +2\right ) c_1 +3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +2\right )^{2}-1}\right )^{{1}/{3}} c_1} \]

✓ Mathematica. Time used: 60.189 (sec). Leaf size: 1624

ode=D[y[x],x]==(2*y[x]-x-4)/(2*x-y[x]+5); 
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) + 4)/(2*x - y(x) + 5) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out