29.20.3 problem 548
Internal
problem
ID
[5144]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
20
Problem
number
:
548
Date
solved
:
Tuesday, March 04, 2025 at 08:12:40 PM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} x \left (x +2 y\right ) y^{\prime }+\left (2 x -y\right ) y&=0 \end{align*}
✓ Maple. Time used: 0.848 (sec). Leaf size: 33
ode:=x*(x+2*y(x))*diff(y(x),x)+(2*x-y(x))*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y \left (x \right ) = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{18}+3 \textit {\_Z}^{3} c_{1} x^{3}-c_{1} x^{3}\right )^{15}}{c_{1} x^{2}}
\]
✓ Mathematica. Time used: 3.342 (sec). Leaf size: 385
ode=x(x+2 y[x])D[y[x],x]+(2 x-y[x])y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,1\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,2\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,3\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,4\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,5\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,6\right ] \\
\end{align*}
✓ Sympy. Time used: 0.762 (sec). Leaf size: 24
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*(x + 2*y(x))*Derivative(y(x), x) + (2*x - y(x))*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (y{\left (x \right )} \right )} = C_{1} + \log {\left (\frac {x}{\left (\frac {x}{y{\left (x \right )}} + \frac {1}{3}\right )^{\frac {5}{3}} y{\left (x \right )}} \right )}
\]