23.1.494 problem 484
Internal
problem
ID
[5101]
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
:
484
Date
solved
:
Tuesday, September 30, 2025 at 11:37:11 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y&=0 \end{align*}
✓ Maple. Time used: 0.019 (sec). Leaf size: 21
ode:=(5-2*x-3*y(x))*diff(y(x),x)+1-2*x-3*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {2 x}{3}-4 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{-\frac {7}{12}+\frac {x}{12}}}{12}\right )-\frac {7}{3}
\]
✓ Mathematica. Time used: 2.183 (sec). Leaf size: 43
ode=(5-2*x-3*y[x])*D[y[x],x]+1-2*x -3*y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to -4 W\left (-e^{\frac {x}{12}-1+c_1}\right )-\frac {2 x}{3}-\frac {7}{3}\\ y(x)&\to \frac {1}{3} (-2 x-7) \end{align*}
✓ Sympy. Time used: 23.580 (sec). Leaf size: 442
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-2*x + (-2*x - 3*y(x) + 5)*Derivative(y(x), x) - 3*y(x) + 1,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {i \sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {i \sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (1 - \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (1 - \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (1 + \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (1 + \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} - i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} - i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} + i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} + i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}\right ]
\]