83.43.12 problem Ex 13 page 14
Internal
problem
ID
[19449]
Book
:
A
Text
book
for
differentional
equations
for
postgraduate
students
by
Ray
and
Chaturvedi.
First
edition,
1958.
BHASKAR
press.
INDIA
Section
:
Book
Solved
Excercises.
Chapter
II.
Equations
of
first
order
and
first
degree
Problem
number
:
Ex
13
page
14
Date
solved
:
Monday, March 31, 2025 at 07:15:02 PM
CAS
classification
:
[[_homogeneous, `class G`], _rational]
\begin{align*} \left (x +2 y^{3}\right ) y^{\prime }&=y \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 220
ode:=(x+2*y(x)^3)*diff(y(x),x) = y(x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {\left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}-12 c_1}{6 \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\
y &= -\frac {i \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}} \sqrt {3}+12 i \sqrt {3}\, c_1 +\left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}-12 c_1}{12 \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\
y &= \frac {i \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}} \sqrt {3}+12 i \sqrt {3}\, c_1 -\left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}+12 c_1}{12 \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\
\end{align*}
✓ Mathematica. Time used: 0.688 (sec). Leaf size: 285
ode=(x+2*y[x]^3)*D[y[x],x]==y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {2 \sqrt [3]{3} c_1-\sqrt [3]{2} \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}}{6^{2/3} \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}} \\
y(x)\to \frac {2^{2/3} \sqrt [3]{3} \left (1-i \sqrt {3}\right ) \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) c_1}{12 \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}} \\
y(x)\to \frac {2^{2/3} \sqrt [3]{3} \left (1+i \sqrt {3}\right ) \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) c_1}{12 \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}} \\
y(x)\to 0 \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((x + 2*y(x)**3)*Derivative(y(x), x) - y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out