29.18.17 problem 493
Internal
problem
ID
[5091]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
18
Problem
number
:
493
Date
solved
:
Tuesday, March 04, 2025 at 07:54:38 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 3 \left (x +2 y\right ) y^{\prime }&=1-x -2 y \end{align*}
✓ Maple. Time used: 0.033 (sec). Leaf size: 23
ode:=3*(x+2*y(x))*diff(y(x),x) = 1-x-2*y(x);
dsolve(ode,y(x), singsol=all);
\[
y \left (x \right ) = -\operatorname {LambertW}\left (-{\mathrm e}^{-\frac {x}{6}-1+\frac {c_{1}}{6}}\right )-1-\frac {x}{2}
\]
✓ Mathematica. Time used: 3.547 (sec). Leaf size: 39
ode=3(x+2 y[x])D[y[x],x]==1-x-2 y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -W\left (-e^{-\frac {x}{6}-1+c_1}\right )-\frac {x}{2}-1 \\
y(x)\to -\frac {x}{2}-1 \\
\end{align*}
✓ Sympy. Time used: 8.640 (sec). Leaf size: 178
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x + (3*x + 6*y(x))*Derivative(y(x), x) + 2*y(x) - 1,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}}}{e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}}}{e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{2 e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{2 e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{2 e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{2 e}\right ) - 1\right ]
\]