74.4.63 problem 60 (b)
Internal
problem
ID
[15877]
Book
:
INTRODUCTORY
DIFFERENTIAL
EQUATIONS.
Martha
L.
Abell,
James
P.
Braselton.
Fourth
edition
2014.
ElScAe.
2014
Section
:
Chapter
2.
First
Order
Equations.
Exercises
2.2,
page
39
Problem
number
:
60
(b)
Date
solved
:
Thursday, March 13, 2025 at 06:55:40 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} y^{\prime }&=\frac {x -y+2}{2 x -2 y-1} \end{align*}
✓ Maple. Time used: 0.065 (sec). Leaf size: 19
ode:=diff(y(x),x) = (x-y(x)+2)/(2*x-2*y(x)-1);
dsolve(ode,y(x), singsol=all);
\[
y = x -\frac {5 \operatorname {LambertW}\left (-\frac {2 c_{1} {\mathrm e}^{\frac {x}{5}-\frac {6}{5}}}{5}\right )}{2}-3
\]
✓ Mathematica. Time used: 3.216 (sec). Leaf size: 33
ode=D[y[x],x]==(x-y[x]+2)/(2*x-2*y[x]-1);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {5}{2} W\left (-e^{\frac {x}{5}-1+c_1}\right )+x-3 \\
y(x)\to x-3 \\
\end{align*}
✓ Sympy. Time used: 10.790 (sec). Leaf size: 230
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-(x - y(x) + 2)/(2*x - 2*y(x) - 1) + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = x - \frac {5 W\left (\frac {2 \sqrt [5]{C_{1} e^{x}}}{5 e^{\frac {6}{5}}}\right )}{2} - 3, \ y{\left (x \right )} = x - \frac {5 W\left (\frac {\sqrt [5]{C_{1} e^{x}} \left (-1 + \sqrt {5} + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right )}{10 e^{\frac {6}{5}}}\right )}{2} - 3, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (1 + \sqrt {5} - \sqrt {2} i \sqrt {5 - \sqrt {5}}\right )}{10 e^{\frac {6}{5}}}\right )}{2} - 3, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (1 + \sqrt {5} + \sqrt {2} i \sqrt {5 - \sqrt {5}}\right )}{10 e^{\frac {6}{5}}}\right )}{2} - 3, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (- \sqrt {5} + 1 + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right )}{10 e^{\frac {6}{5}}}\right )}{2} - 3\right ]
\]