26.1.9 problem 5.b
Internal
problem
ID
[4249]
Book
:
Differential
equations
with
applications
and
historial
notes,
George
F.
Simmons.
Second
edition.
1971
Section
:
Chapter
2,
section
7,
page
37
Problem
number
:
5.b
Date
solved
:
Tuesday, March 04, 2025 at 05:59:51 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} y^{\prime }&=\frac {x +y+4}{x +y-6} \end{align*}
✓ Maple. Time used: 0.023 (sec). Leaf size: 21
ode:=diff(y(x),x) = (x+y(x)+4)/(x+y(x)-6);
dsolve(ode,y(x), singsol=all);
\[
y \left (x \right ) = -x -5 \operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{-\frac {2 x}{5}+\frac {1}{5}}}{5}\right )+1
\]
✓ Mathematica. Time used: 3.596 (sec). Leaf size: 35
ode=D[y[x],x]==(x+y[x]+4)/(x+y[x]-6);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -5 W\left (-e^{-\frac {2 x}{5}-1+c_1}\right )-x+1 \\
y(x)\to 1-x \\
\end{align*}
✓ Sympy. Time used: 7.000 (sec). Leaf size: 228
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(Derivative(y(x), x) - (x + y(x) + 4)/(x + y(x) - 6),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - x - 5 W\left (\frac {\sqrt [5]{C_{1} e^{- 2 x}} e^{\frac {1}{5}}}{10}\right ) + 1, \ y{\left (x \right )} = - x - 5 W\left (\frac {\sqrt [5]{C_{1} e^{- 2 x}} \left (-1 + \sqrt {5} + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right ) e^{\frac {1}{5}}}{40}\right ) + 1, \ y{\left (x \right )} = - x - 5 W\left (- \frac {\sqrt [5]{C_{1} e^{- 2 x}} \left (1 + \sqrt {5} - \sqrt {2} i \sqrt {5 - \sqrt {5}}\right ) e^{\frac {1}{5}}}{40}\right ) + 1, \ y{\left (x \right )} = - x - 5 W\left (- \frac {\sqrt [5]{C_{1} e^{- 2 x}} \left (1 + \sqrt {5} + \sqrt {2} i \sqrt {5 - \sqrt {5}}\right ) e^{\frac {1}{5}}}{40}\right ) + 1, \ y{\left (x \right )} = - x - 5 W\left (- \frac {\sqrt [5]{C_{1} e^{- 2 x}} \left (- \sqrt {5} + 1 + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right ) e^{\frac {1}{5}}}{40}\right ) + 1\right ]
\]