60.1.20 problem Problem 28
Internal
problem
ID
[15148]
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
:
Thursday, October 02, 2025 at 10:04:36 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: 60.115 (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. Time used: 103.056 (sec). Leaf size: 372
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)
\[
\left [ y{\left (x \right )} = \frac {- \frac {2 \cdot 3^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 108 x + 108} + 18\right )}} - \sqrt {3} x + i x + \frac {3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 108 x + 108} + 18\right )}}{3} + \frac {\sqrt [3]{3} i \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 108 x + 108} + 18\right )}}{3} - \sqrt {3} + i}{\sqrt {3} - i}, \ y{\left (x \right )} = \frac {\frac {2 \cdot 3^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 108 x + 108} + 18\right )}} - \sqrt {3} x - i x + \frac {3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 108 x + 108} + 18\right )}}{3} - \frac {\sqrt [3]{3} i \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 108 x + 108} + 18\right )}}{3} - \sqrt {3} - i}{\sqrt {3} + i}, \ y{\left (x \right )} = - \frac {3^{\frac {2}{3}} C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 108 x + 108} + 18\right )}} - x - \frac {\sqrt [3]{3} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 108 x + 108} + 18\right )}}{3} - 1\right ]
\]