62.12.22 problem Ex 23
Internal
problem
ID
[12789]
Book
:
An
elementary
treatise
on
differential
equations
by
Abraham
Cohen.
DC
heath
publishers.
1906
Section
:
Chapter
2,
differential
equations
of
the
first
order
and
the
first
degree.
Article
19.
Summary.
Page
29
Problem
number
:
Ex
23
Date
solved
:
Wednesday, March 05, 2025 at 08:30:52 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.068 (sec). Leaf size: 21
ode:=2*x+3*y(x)-1+(2*x+3*y(x)-5)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {2 x}{3}-4 \operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {x}{12}-\frac {7}{12}}}{12}\right )-\frac {7}{3}
\]
✓ Mathematica. Time used: 0.938 (sec). Leaf size: 43
ode=(2*x+3*y[x]-1)+(2*x+3*y[x]-5)*D[y[x],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: 33.617 (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)
\[
\left [ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {i \sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {i \sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (1 - \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (1 - \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (1 + \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (1 + \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} - i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} - i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} + i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} + i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}\right ]
\]