29.8.21 problem 226
Internal
problem
ID
[4826]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
8
Problem
number
:
226
Date
solved
:
Sunday, March 30, 2025 at 04:02:32 AM
CAS
classification
:
[_rational, _Bernoulli]
\begin{align*} \left (1+x \right ) y^{\prime }&=\left (1-x y^{3}\right ) y \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 178
ode:=(1+x)*diff(y(x),x) = (1-x*y(x)^3)*y(x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {2^{{2}/{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_1 \right )^{2}\right )}^{{1}/{3}} \left (1+x \right )}{3 x^{4}+8 x^{3}+6 x^{2}+4 c_1} \\
y &= -\frac {{\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_1 \right )^{2}\right )}^{{1}/{3}} 2^{{2}/{3}} \left (1+i \sqrt {3}\right ) \left (1+x \right )}{6 x^{4}+16 x^{3}+12 x^{2}+8 c_1} \\
y &= \frac {{\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_1 \right )^{2}\right )}^{{1}/{3}} 2^{{2}/{3}} \left (i \sqrt {3}-1\right ) \left (1+x \right )}{6 x^{4}+16 x^{3}+12 x^{2}+8 c_1} \\
\end{align*}
✓ Mathematica. Time used: 0.295 (sec). Leaf size: 124
ode=(1+x) D[y[x],x]==(1-x y[x]^3)y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {(-2)^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} \\
y(x)\to -\frac {2^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} \\
y(x)\to \frac {\sqrt [3]{-1} 2^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} \\
y(x)\to 0 \\
\end{align*}
✓ Sympy. Time used: 2.524 (sec). Leaf size: 133
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((x + 1)*Derivative(y(x), x) - (-x*y(x)**3 + 1)*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = 2^{\frac {2}{3}} \left (x + 1\right ) \sqrt [3]{\frac {1}{C_{1} + 3 x^{4} + 8 x^{3} + 6 x^{2}}}, \ y{\left (x \right )} = \frac {2^{\frac {2}{3}} \left (- x + \sqrt {3} i x - 1 + \sqrt {3} i\right ) \sqrt [3]{\frac {1}{C_{1} + 3 x^{4} + 8 x^{3} + 6 x^{2}}}}{2}, \ y{\left (x \right )} = \frac {2^{\frac {2}{3}} \left (- x - \sqrt {3} i x - 1 - \sqrt {3} i\right ) \sqrt [3]{\frac {1}{C_{1} + 3 x^{4} + 8 x^{3} + 6 x^{2}}}}{2}\right ]
\]