30.1.3 problem Example, page 28
Internal
problem
ID
[5691]
Book
:
Differential
and
integral
calculus,
vol
II
By
N.
Piskunov.
1974
Section
:
Chapter
1
Problem
number
:
Example,
page
28
Date
solved
:
Sunday, March 30, 2025 at 10:02:32 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} y^{\prime }&=\frac {2 x +y-1}{4 x +2 y+5} \end{align*}
✓ Maple. Time used: 0.026 (sec). Leaf size: 23
ode:=diff(y(x),x) = (2*x+y(x)-1)/(4*x+2*y(x)+5);
dsolve(ode,y(x), singsol=all);
\[
y = \frac {7 \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {18}{7}+\frac {25 x}{7}-\frac {25 c_1}{7}}}{7}\right )}{10}-\frac {9}{5}-2 x
\]
✓ Mathematica. Time used: 3.757 (sec). Leaf size: 41
ode=D[y[x],x]==(2*x+y[x]-1)/(4*x+2*y[x]+5);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {7}{10} W\left (-e^{\frac {25 x}{7}-1+c_1}\right )-2 x-\frac {9}{5} \\
y(x)\to -2 x-\frac {9}{5} \\
\end{align*}
✓ Sympy. Time used: 64.594 (sec). Leaf size: 287
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((-2*x - y(x) + 1)/(4*x + 2*y(x) + 5) + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - 2 x + \frac {7 W\left (- \frac {2 \sqrt [7]{C_{1} e^{25 x}} e^{\frac {18}{7}}}{35}\right )}{10} - \frac {9}{5}, \ y{\left (x \right )} = - 2 x + \frac {7 W\left (- \frac {2 \sqrt [7]{C_{1} e^{25 x}} e^{\frac {18}{7} - \frac {2 i \pi }{7}}}{35}\right )}{10} - \frac {9}{5}, \ y{\left (x \right )} = - 2 x + \frac {7 W\left (\frac {2 \sqrt [7]{C_{1} e^{25 x}} e^{\frac {18}{7} - \frac {i \pi }{7}}}{35}\right )}{10} - \frac {9}{5}, \ y{\left (x \right )} = - 2 x + \frac {7 W\left (\frac {2 \sqrt [7]{C_{1} e^{25 x}} e^{\frac {18}{7} + \frac {i \pi }{7}}}{35}\right )}{10} - \frac {9}{5}, \ y{\left (x \right )} = - 2 x + \frac {7 W\left (\frac {2 \sqrt [7]{C_{1} e^{25 x}} \left (\sin {\left (\frac {\pi }{14} \right )} - i \cos {\left (\frac {\pi }{14} \right )}\right ) e^{\frac {18}{7}}}{35}\right )}{10} - \frac {9}{5}, \ y{\left (x \right )} = - 2 x + \frac {7 W\left (\frac {2 \sqrt [7]{C_{1} e^{25 x}} \left (\sin {\left (\frac {\pi }{14} \right )} + i \cos {\left (\frac {\pi }{14} \right )}\right ) e^{\frac {18}{7}}}{35}\right )}{10} - \frac {9}{5}, \ y{\left (x \right )} = - 2 x + \frac {7 W\left (- \frac {2 \sqrt [7]{C_{1} e^{25 x}} \left (\sin {\left (\frac {3 \pi }{14} \right )} + i \cos {\left (\frac {3 \pi }{14} \right )}\right ) e^{\frac {18}{7}}}{35}\right )}{10} - \frac {9}{5}\right ]
\]