23.1.564 problem 554
Internal
problem
ID
[5171]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Part
II.
Chapter
1.
THE
DIFFERENTIAL
EQUATION
IS
OF
FIRST
ORDER
AND
OF
FIRST
DEGREE,
page
223
Problem
number
:
554
Date
solved
:
Tuesday, September 30, 2025 at 11:49:00 AM
CAS
classification
:
[_rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} x \left (1-x -2 y\right ) y^{\prime }+\left (1+2 x +y\right ) y&=0 \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 386
ode:=x*(1-x-2*y(x))*diff(y(x),x)+(1+2*x+y(x))*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {3 \,5^{{1}/{3}} {\left (x \left (\sqrt {5}\, \sqrt {\frac {80 c_1 \,x^{2}-160 c_1 x +80 c_1 -x}{c_1}}+20 x -20\right ) c_1^{2}\right )}^{{1}/{3}}}{40 c_1}+\frac {3 x 5^{{2}/{3}}}{40 {\left (x \left (\sqrt {5}\, \sqrt {\frac {80 c_1 \,x^{2}-160 c_1 x +80 c_1 -x}{c_1}}+20 x -20\right ) c_1^{2}\right )}^{{1}/{3}}}+x -1 \\
y &= \frac {-\frac {3 \left (1+i \sqrt {3}\right ) 5^{{1}/{3}} {\left (x \left (\sqrt {5}\, \sqrt {\frac {80 \left (-1+x \right )^{2} c_1 -x}{c_1}}+20 x -20\right ) c_1^{2}\right )}^{{2}/{3}}}{80}+\frac {3 c_1 \left (\frac {80 \left (-1+x \right ) {\left (x \left (\sqrt {5}\, \sqrt {\frac {80 \left (-1+x \right )^{2} c_1 -x}{c_1}}+20 x -20\right ) c_1^{2}\right )}^{{1}/{3}}}{3}+x 5^{{2}/{3}} \left (i \sqrt {3}-1\right )\right )}{80}}{c_1 {\left (x \left (\sqrt {5}\, \sqrt {\frac {80 \left (-1+x \right )^{2} c_1 -x}{c_1}}+20 x -20\right ) c_1^{2}\right )}^{{1}/{3}}} \\
y &= \frac {\frac {3 \left (i \sqrt {3}-1\right ) 5^{{1}/{3}} {\left (x \left (\sqrt {5}\, \sqrt {\frac {80 \left (-1+x \right )^{2} c_1 -x}{c_1}}+20 x -20\right ) c_1^{2}\right )}^{{2}/{3}}}{80}+\frac {3 \left (-\frac {80 \left (1-x \right ) {\left (x \left (\sqrt {5}\, \sqrt {\frac {80 \left (-1+x \right )^{2} c_1 -x}{c_1}}+20 x -20\right ) c_1^{2}\right )}^{{1}/{3}}}{3}+\left (-i \sqrt {3}-1\right ) x 5^{{2}/{3}}\right ) c_1}{80}}{c_1 {\left (x \left (\sqrt {5}\, \sqrt {\frac {80 \left (-1+x \right )^{2} c_1 -x}{c_1}}+20 x -20\right ) c_1^{2}\right )}^{{1}/{3}}} \\
\end{align*}
✓ Mathematica. Time used: 7.812 (sec). Leaf size: 126
ode=x*(1-x-2*y[x])*D[y[x],x]+(1+2*x+y[x])*y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^x-\frac {\sqrt [3]{2} 5^{2/3} \left (-(K[2]+1)^3\right )^{2/3}}{27 K[2]-27 K[2]^3}dK[2]+c_1=\int _1^{\frac {(x+1) (5 x-8 y(x)-5)}{2^{2/3} \sqrt [3]{5} \sqrt [3]{-(x+1)^3} (x+2 y(x)-1)}}\frac {1}{K[1]^3+\frac {21 \sqrt [3]{-\frac {1}{2}} K[1]}{2\ 5^{2/3}}+1}dK[1],y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*(-x - 2*y(x) + 1)*Derivative(y(x), x) + (2*x + y(x) + 1)*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out