23.1.490 problem 480
Internal
problem
ID
[5097]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Part
II.
Chapter
1.
THE
DIFFERENTIAL
EQUATION
IS
OF
FIRST
ORDER
AND
OF
FIRST
DEGREE,
page
223
Problem
number
:
480
Date
solved
:
Tuesday, September 30, 2025 at 11:36:19 AM
CAS
classification
:
[_separable]
\begin{align*} 3 \left (2-y\right ) y^{\prime }+x y&=0 \end{align*}
✓ Maple. Time used: 0.012 (sec). Leaf size: 19
ode:=3*(2-y(x))*diff(y(x),x)+x*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x^{2}}{12}-\frac {c_1}{6}}}{2}\right )
\]
✓ Mathematica. Time used: 0.068 (sec). Leaf size: 39
ode=3*(2-y[x])*D[y[x],x]+x*y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]-2}{K[1]}dK[1]\&\right ]\left [\frac {x^2}{6}+c_1\right ]\\ y(x)&\to 0 \end{align*}
✓ Sympy. Time used: 27.086 (sec). Leaf size: 296
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*y(x) + (6 - 3*y(x))*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - 2 W\left (- \frac {i \sqrt [12]{C_{1} e^{- x^{2}}}}{2}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {i \sqrt [12]{C_{1} e^{- x^{2}}}}{2}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (-1 + \sqrt {3} i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (1 - \sqrt {3} i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (-1 - \sqrt {3} i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (1 + \sqrt {3} i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (- \sqrt {3} + i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (\sqrt {3} - i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (- \sqrt {3} - i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (\sqrt {3} + i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (- \frac {\sqrt [12]{C_{1} e^{- x^{2}}}}{2}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}}}{2}\right )\right ]
\]