15.3.9 problem 9
Internal
problem
ID
[2902]
Book
:
Differential
Equations
by
Alfred
L.
Nelson,
Karl
W.
Folley,
Max
Coral.
3rd
ed.
DC
heath.
Boston.
1964
Section
:
Exercise
7,
page
28
Problem
number
:
9
Date
solved
:
Tuesday, March 04, 2025 at 03:07:10 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: 0.019 (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);
\[
y = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x}{6}-\frac {3}{2}+\frac {c_1}{6}}}{2}\right )-\frac {3}{2}-\frac {x}{2}
\]
✓ Mathematica. Time used: 4.053 (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: 8.872 (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)
\[
\left [ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}}}{2 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}}}{2 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{4 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{4 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{4 e^{\frac {3}{2}}}\right ) - \frac {3}{2}, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{4 e^{\frac {3}{2}}}\right ) - \frac {3}{2}\right ]
\]