32.2.8 problem Differential equations with Linear Coefficients. Exercise 8.8, page 69
Internal
problem
ID
[5792]
Book
:
Ordinary
Differential
Equations,
By
Tenenbaum
and
Pollard.
Dover,
NY
1963
Section
:
Chapter
2.
Special
types
of
differential
equations
of
the
first
kind.
Lesson
8
Problem
number
:
Differential
equations
with
Linear
Coefficients.
Exercise
8.8,
page
69
Date
solved
:
Tuesday, March 04, 2025 at 11:45:20 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.036 (sec). Leaf size: 23
ode:=x+2*y(x)+(3*x+6*y(x)+3)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x}{6}-\frac {3}{2}+\frac {c_{1}}{6}}}{2}\right )-\frac {3}{2}-\frac {x}{2}
\]
✓ Mathematica. Time used: 4.624 (sec). Leaf size: 43
ode=(x+2*y[x])+(3*x+6*y[x]+3)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {1}{2} \left (-2 W\left (-e^{-\frac {x}{6}-1+c_1}\right )-x-3\right ) \\
y(x)\to \frac {1}{2} (-x-3) \\
\end{align*}
✓ Sympy. Time used: 8.512 (sec). Leaf size: 202
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x + (3*x + 6*y(x) + 3)*Derivative(y(x), x) + 2*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}}}{2 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}}}{2 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{4 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{4 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{4 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{4 e^{\frac {3}{2}}}\right ) - \frac {3}{2}\right ]
\]