77.4.3 problem 3
Internal
problem
ID
[20360]
Book
:
A
Text
book
for
differentional
equations
for
postgraduate
students
by
Ray
and
Chaturvedi.
First
edition,
1958.
BHASKAR
press.
INDIA
Section
:
Chapter
II.
Equations
of
first
order
and
first
degree.
Exercise
II
(C)
at
page
12
Problem
number
:
3
Date
solved
:
Thursday, October 02, 2025 at 05:47:16 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: 0.021 (sec). Leaf size: 21
ode:=(2*x+3*y(x)-5)*diff(y(x),x)+2*x+3*y(x)-1 = 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: 2.311 (sec). Leaf size: 43
ode=(2*x+3*y[x]-5)*D[y[x],x]+(2*x+3*y[x]-1)==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: 23.906 (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)
\[
\left [ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {i \sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {i \sqrt [12]{C_{1} e^{x}}}{12 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (1 - \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (1 - \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (1 + \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (1 + \sqrt {3} i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} - i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} - i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (- \frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} + i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - 4 W\left (\frac {\sqrt [12]{C_{1} e^{x}} \left (\sqrt {3} + i\right )}{24 e^{\frac {7}{12}}}\right ) - \frac {7}{3}\right ]
\]