76.12.30 problem Ex. 33
Internal
problem
ID
[20080]
Book
:
Introductory
Course
On
Differential
Equations
by
Daniel
A
Murray.
Longmans
Green
and
Co.
NY.
1924
Section
:
Chapter
II.
Equations
of
the
first
order
and
of
the
first
degree.
Examples
on
chapter
II
at
page
29
Problem
number
:
Ex.
33
Date
solved
:
Thursday, October 02, 2025 at 05:22:18 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.024 (sec). Leaf size: 23
ode:=3*y(x)+2*x+4-(4*x+6*y(x)+5)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {3 \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{-\frac {44}{9}-\frac {49 x}{9}+\frac {49 c_1}{9}}}{9}\right )}{14}-\frac {22}{21}-\frac {2 x}{3}
\]
✓ Mathematica. Time used: 2.476 (sec). Leaf size: 43
ode=(3*y[x]+2*x+4)-(4*x+6*y[x]+5)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \frac {1}{42} \left (-9 W\left (-e^{-\frac {49 x}{9}-1+c_1}\right )-28 x-44\right )\\ y(x)&\to -\frac {2}{21} (7 x+11) \end{align*}
✓ Sympy. Time used: 47.099 (sec). Leaf size: 393
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(2*x - (4*x + 6*y(x) + 5)*Derivative(y(x), x) + 3*y(x) + 4,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (\frac {2 \sqrt [9]{C_{1} e^{- 49 x}}}{9 e^{\frac {44}{9}}}\right )}{14} - \frac {22}{21}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (\frac {2 \sqrt [9]{C_{1} e^{- 49 x}} e^{- \frac {44}{9} - \frac {2 i \pi }{9}}}{9}\right )}{14} - \frac {22}{21}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (- \frac {2 \sqrt [9]{C_{1} e^{- 49 x}} e^{- \frac {44}{9} - \frac {i \pi }{9}}}{9}\right )}{14} - \frac {22}{21}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (- \frac {2 \sqrt [9]{C_{1} e^{- 49 x}} e^{- \frac {44}{9} + \frac {i \pi }{9}}}{9}\right )}{14} - \frac {22}{21}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (\frac {2 \sqrt [9]{C_{1} e^{- 49 x}} e^{- \frac {44}{9} + \frac {2 i \pi }{9}}}{9}\right )}{14} - \frac {22}{21}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (- \frac {\sqrt [9]{C_{1} e^{- 49 x}} \left (1 - \sqrt {3} i\right )}{9 e^{\frac {44}{9}}}\right )}{14} - \frac {22}{21}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (- \frac {\sqrt [9]{C_{1} e^{- 49 x}} \left (1 + \sqrt {3} i\right )}{9 e^{\frac {44}{9}}}\right )}{14} - \frac {22}{21}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (\frac {2 \sqrt [9]{C_{1} e^{- 49 x}} \left (\sin {\left (\frac {\pi }{18} \right )} - i \cos {\left (\frac {\pi }{18} \right )}\right )}{9 e^{\frac {44}{9}}}\right )}{14} - \frac {22}{21}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {3 W\left (\frac {2 \sqrt [9]{C_{1} e^{- 49 x}} \left (\sin {\left (\frac {\pi }{18} \right )} + i \cos {\left (\frac {\pi }{18} \right )}\right )}{9 e^{\frac {44}{9}}}\right )}{14} - \frac {22}{21}\right ]
\]