56.12.11 problem Ex 12
Internal
problem
ID
[14138]
Book
:
An
elementary
treatise
on
differential
equations
by
Abraham
Cohen.
DC
heath
publishers.
1906
Section
:
Chapter
2,
differential
equations
of
the
first
order
and
the
first
degree.
Article
19.
Summary.
Page
29
Problem
number
:
Ex
12
Date
solved
:
Thursday, October 02, 2025 at 09:16:06 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \end{align*}
✓ Maple. Time used: 0.223 (sec). Leaf size: 115
ode:=x-2*y(x)+5+(2*x-y(x)+4)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {\frac {1}{2}+\frac {\left (1-i \sqrt {3}\right ) \left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +1\right )^{2}-1}+27 \left (x +1\right ) c_1 \right )^{{2}/{3}}}{6}+\frac {i \sqrt {3}}{2}-\left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +1\right )^{2}-1}+27 c_1 x +27 c_1 \right )^{{1}/{3}} \left (x -1\right ) c_1}{\left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x +1\right )^{2}-1}+27 \left (x +1\right ) c_1 \right )^{{1}/{3}} c_1}
\]
✓ Mathematica. Time used: 60.121 (sec). Leaf size: 1601
ode=(x-2*y[x]+5)+(2*x-y[x]+4)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Too large to display
✓ Sympy. Time used: 101.927 (sec). Leaf size: 371
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x + (2*x - y(x) + 4)*Derivative(y(x), x) - 2*y(x) + 5,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {- \frac {2 \cdot 3^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 54 x + 27} + 9\right )}} - \sqrt {3} x + i x + \frac {3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 54 x + 27} + 9\right )}}{3} + \frac {\sqrt [3]{3} i \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 54 x + 27} + 9\right )}}{3} + \sqrt {3} - i}{\sqrt {3} - i}, \ y{\left (x \right )} = \frac {\frac {2 \cdot 3^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 54 x + 27} + 9\right )}} - \sqrt {3} x - i x + \frac {3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 54 x + 27} + 9\right )}}{3} - \frac {\sqrt [3]{3} i \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 54 x + 27} + 9\right )}}{3} + \sqrt {3} + i}{\sqrt {3} + i}, \ y{\left (x \right )} = - \frac {3^{\frac {2}{3}} C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 54 x + 27} + 9\right )}} - x - \frac {\sqrt [3]{3} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {- C_{1} + 27 x^{2} + 54 x + 27} + 9\right )}}{3} + 1\right ]
\]