83.9.10 problem 10
Internal
problem
ID
[21968]
Book
:
Differential
Equations
By
Kaj
L.
Nielsen.
Second
edition
1966.
Barnes
and
nobel.
66-28306
Section
:
Chapter
III.
First
order
differential
equations
of
the
first
degree.
Ex.
X
at
page
57
Problem
number
:
10
Date
solved
:
Thursday, October 02, 2025 at 08:20:33 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 3 x +3 y-2+\left (2 x +2 y+1\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.014 (sec). Leaf size: 21
ode:=3*x+3*y(x)-2+(2*x+2*y(x)+1)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -x +\frac {7 \operatorname {LambertW}\left (\frac {2 c_1 \,{\mathrm e}^{-\frac {6}{7}-\frac {x}{7}}}{7}\right )}{2}+3
\]
✓ Mathematica. Time used: 2.15 (sec). Leaf size: 37
ode=(3*x+3*y[x]-2)+(2*x+2*y[x]+1)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \frac {7}{2} W\left (-e^{-\frac {x}{7}-1+c_1}\right )-x+3\\ y(x)&\to 3-x \end{align*}
✓ Sympy. Time used: 36.627 (sec). Leaf size: 255
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(3*x + (2*x + 2*y(x) + 1)*Derivative(y(x), x) + 3*y(x) - 2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - x + \frac {7 W\left (- \frac {2 \sqrt [7]{C_{1} e^{- x}}}{7 e^{\frac {6}{7}}}\right )}{2} + 3, \ y{\left (x \right )} = - x + \frac {7 W\left (- \frac {2 \sqrt [7]{C_{1} e^{- x}} e^{- \frac {6}{7} - \frac {2 i \pi }{7}}}{7}\right )}{2} + 3, \ y{\left (x \right )} = - x + \frac {7 W\left (\frac {2 \sqrt [7]{C_{1} e^{- x}} e^{- \frac {6}{7} - \frac {i \pi }{7}}}{7}\right )}{2} + 3, \ y{\left (x \right )} = - x + \frac {7 W\left (\frac {2 \sqrt [7]{C_{1} e^{- x}} e^{- \frac {6}{7} + \frac {i \pi }{7}}}{7}\right )}{2} + 3, \ y{\left (x \right )} = - x + \frac {7 W\left (\frac {2 \sqrt [7]{C_{1} e^{- x}} \left (\sin {\left (\frac {\pi }{14} \right )} - i \cos {\left (\frac {\pi }{14} \right )}\right )}{7 e^{\frac {6}{7}}}\right )}{2} + 3, \ y{\left (x \right )} = - x + \frac {7 W\left (\frac {2 \sqrt [7]{C_{1} e^{- x}} \left (\sin {\left (\frac {\pi }{14} \right )} + i \cos {\left (\frac {\pi }{14} \right )}\right )}{7 e^{\frac {6}{7}}}\right )}{2} + 3, \ y{\left (x \right )} = - x + \frac {7 W\left (- \frac {2 \sqrt [7]{C_{1} e^{- x}} \left (\sin {\left (\frac {3 \pi }{14} \right )} + i \cos {\left (\frac {3 \pi }{14} \right )}\right )}{7 e^{\frac {6}{7}}}\right )}{2} + 3\right ]
\]