29.18.4 problem 480
Internal
problem
ID
[5078]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
18
Problem
number
:
480
Date
solved
:
Sunday, March 30, 2025 at 06:35:40 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (2+2 x +3 y\right ) y^{\prime }&=1-2 x -3 y \end{align*}
✓ Maple. Time used: 0.019 (sec). Leaf size: 21
ode:=(2+2*x+3*y(x))*diff(y(x),x) = 1-2*x-3*y(x);
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {2 x}{3}+3 \operatorname {LambertW}\left (\frac {c_1 \,{\mathrm e}^{-\frac {7}{9}-\frac {x}{9}}}{9}\right )+\frac {7}{3}
\]
✓ Mathematica. Time used: 4.158 (sec). Leaf size: 43
ode=(2+2 x+3 y[x])D[y[x],x]==1-2 x-3 y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {1}{3} \left (9 W\left (-e^{-\frac {x}{9}-1+c_1}\right )-2 x+7\right ) \\
y(x)\to \frac {1}{3} (7-2 x) \\
\end{align*}
✓ Sympy. Time used: 62.213 (sec). Leaf size: 335
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(2*x + (2*x + 3*y(x) + 2)*Derivative(y(x), x) + 3*y(x) - 1,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (- \frac {\sqrt [9]{C_{1} e^{- x}}}{9 e^{\frac {7}{9}}}\right ) + \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (- \frac {\sqrt [9]{C_{1} e^{- x}} e^{- \frac {7}{9} - \frac {2 i \pi }{9}}}{9}\right ) + \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (\frac {\sqrt [9]{C_{1} e^{- x}} e^{- \frac {7}{9} - \frac {i \pi }{9}}}{9}\right ) + \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (\frac {\sqrt [9]{C_{1} e^{- x}} e^{- \frac {7}{9} + \frac {i \pi }{9}}}{9}\right ) + \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (- \frac {\sqrt [9]{C_{1} e^{- x}} e^{- \frac {7}{9} + \frac {2 i \pi }{9}}}{9}\right ) + \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (\frac {\sqrt [9]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{18 e^{\frac {7}{9}}}\right ) + \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (\frac {\sqrt [9]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{18 e^{\frac {7}{9}}}\right ) + \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (\frac {\sqrt [9]{C_{1} e^{- x}} \left (- \sin {\left (\frac {\pi }{18} \right )} + i \cos {\left (\frac {\pi }{18} \right )}\right )}{9 e^{\frac {7}{9}}}\right ) + \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (- \frac {\sqrt [9]{C_{1} e^{- x}} \left (\sin {\left (\frac {\pi }{18} \right )} + i \cos {\left (\frac {\pi }{18} \right )}\right )}{9 e^{\frac {7}{9}}}\right ) + \frac {7}{3}\right ]
\]