60.2.173 problem 749
Internal
problem
ID
[10747]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
749
Date
solved
:
Friday, March 14, 2025 at 02:27:25 AM
CAS
classification
:
[_rational]
\begin{align*} y^{\prime }&=\frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y} \end{align*}
✓ Maple. Time used: 0.014 (sec). Leaf size: 186
ode:=diff(y(x),x) = (x-y(x))^2*(x+y(x))^2*x/y(x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {\sqrt {\left (c_{1} \left (x^{2}+1\right ) {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+\left (x^{2}-1\right ) {\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right ) \left (c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right )}}{c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}} \\
y &= -\frac {\sqrt {\left (c_{1} \left (x^{2}+1\right ) {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+\left (x^{2}-1\right ) {\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right ) \left (c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}\right )}}{c_{1} {\mathrm e}^{-\frac {\left (x^{2}+1\right )^{2}}{2}}+{\mathrm e}^{-\frac {x^{2} \left (x^{2}-2\right )}{2}}} \\
\end{align*}
✓ Mathematica. Time used: 0.161 (sec). Leaf size: 155
ode=D[y[x],x] == (x*(x - y[x])^2*(x + y[x])^2)/y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{2 \left (-x^2+K[2]^2-1\right )}-\frac {K[2]}{2 \left (-x^2+K[2]^2+1\right )}-\int _1^x\left (\frac {K[1] K[2]}{\left (K[1]^2-K[2]^2+1\right )^2}-\frac {K[1] K[2]}{\left (K[1]^2-K[2]^2-1\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\left (-\frac {K[1]}{2 \left (K[1]^2-y(x)^2-1\right )}+\frac {K[1]}{2 \left (K[1]^2-y(x)^2+1\right )}-K[1]\right )dK[1]=c_1,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x*(x - y(x))**2*(x + y(x))**2/y(x) + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : The given ODE -x**5/y(x) + 2*x**3*y(x) - x*y(x)**3 + Derivative(y(x), x) cannot be solved by the factorable group method