89.7.19 problem 19
Internal
problem
ID
[24450]
Book
:
A
short
course
in
Differential
Equations.
Earl
D.
Rainville.
Second
edition.
1958.
Macmillan
Publisher,
NY.
CAT
58-5010
Section
:
Chapter
4.
Additional
topics
on
equations
of
first
order
and
first
degree.
Exercises
at
page
61
Problem
number
:
19
Date
solved
:
Thursday, October 02, 2025 at 10:36:41 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} x +2 y-1-\left (x +2 y-5\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.015 (sec). Leaf size: 21
ode:=x+2*y(x)-1-(x+2*y(x)-5)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {x}{2}-\frac {4 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{\frac {7}{8}-\frac {9 x}{8}}}{8}\right )}{3}+\frac {7}{6}
\]
✓ Mathematica. Time used: 2.406 (sec). Leaf size: 43
ode=( x+2*y[x]-1)-(x+2*y[x]-5)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \frac {1}{6} \left (-8 W\left (-e^{-\frac {9 x}{8}-1+c_1}\right )-3 x+7\right )\\ y(x)&\to \frac {1}{6} (7-3 x) \end{align*}
✓ Sympy. Time used: 12.037 (sec). Leaf size: 289
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x - (x + 2*y(x) - 5)*Derivative(y(x), x) + 2*y(x) - 1,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {x}{2} - \frac {4 W\left (- \frac {\sqrt [8]{C_{1} e^{- 9 x}} e^{\frac {7}{8}}}{8}\right )}{3} + \frac {7}{6}, \ y{\left (x \right )} = - \frac {x}{2} - \frac {4 W\left (\frac {\sqrt [8]{C_{1} e^{- 9 x}} e^{\frac {7}{8}}}{8}\right )}{3} + \frac {7}{6}, \ y{\left (x \right )} = - \frac {x}{2} - \frac {4 W\left (- \frac {i \sqrt [8]{C_{1} e^{- 9 x}} e^{\frac {7}{8}}}{8}\right )}{3} + \frac {7}{6}, \ y{\left (x \right )} = - \frac {x}{2} - \frac {4 W\left (\frac {i \sqrt [8]{C_{1} e^{- 9 x}} e^{\frac {7}{8}}}{8}\right )}{3} + \frac {7}{6}, \ y{\left (x \right )} = - \frac {x}{2} - \frac {4 W\left (- \frac {\sqrt {2} \sqrt [8]{C_{1} e^{- 9 x}} \left (1 - i\right ) e^{\frac {7}{8}}}{16}\right )}{3} + \frac {7}{6}, \ y{\left (x \right )} = - \frac {x}{2} - \frac {4 W\left (\frac {\sqrt {2} \sqrt [8]{C_{1} e^{- 9 x}} \left (1 - i\right ) e^{\frac {7}{8}}}{16}\right )}{3} + \frac {7}{6}, \ y{\left (x \right )} = - \frac {x}{2} - \frac {4 W\left (- \frac {\sqrt {2} \sqrt [8]{C_{1} e^{- 9 x}} \left (1 + i\right ) e^{\frac {7}{8}}}{16}\right )}{3} + \frac {7}{6}, \ y{\left (x \right )} = - \frac {x}{2} - \frac {4 W\left (\frac {\sqrt {2} \sqrt [8]{C_{1} e^{- 9 x}} \left (1 + i\right ) e^{\frac {7}{8}}}{16}\right )}{3} + \frac {7}{6}\right ]
\]