29.18.1 problem 477
Internal
problem
ID
[5075]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
18
Problem
number
:
477
Date
solved
:
Sunday, March 30, 2025 at 06:35:31 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: 19.238 (sec). Leaf size: 64
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 -2 W\left (-\frac {1}{2} \sqrt {e^{-\frac {x^2}{6}-c_1}}\right ) \\
y(x)\to -2 W\left (\frac {1}{2} \sqrt {e^{-\frac {x^2}{6}-c_1}}\right ) \\
y(x)\to 0 \\
\end{align*}
✓ Sympy. Time used: 37.425 (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)
\[
\left [ y{\left (x \right )} = - 2 W\left (- \frac {i \sqrt [12]{C_{1} e^{- x^{2}}}}{2}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {i \sqrt [12]{C_{1} e^{- x^{2}}}}{2}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (-1 + \sqrt {3} i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (1 - \sqrt {3} i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (-1 - \sqrt {3} i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (1 + \sqrt {3} i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (- \sqrt {3} + i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (\sqrt {3} - i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (- \sqrt {3} - i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}} \left (\sqrt {3} + i\right )}{4}\right ), \ y{\left (x \right )} = - 2 W\left (- \frac {\sqrt [12]{C_{1} e^{- x^{2}}}}{2}\right ), \ y{\left (x \right )} = - 2 W\left (\frac {\sqrt [12]{C_{1} e^{- x^{2}}}}{2}\right )\right ]
\]