29.22.10 problem 616

Internal problem ID [5210]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 616
Date solved : Sunday, March 30, 2025 at 06:52:31 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (x^{2}+2 x y-y^{2}\right ) y^{\prime }+x^{2}-2 x y+y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

ode:=(x^2+2*x*y(x)-y(x)^2)*diff(y(x),x)+x^2-2*x*y(x)+y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}-2 \textit {\_a} -1}{\textit {\_a}^{3}-3 \textit {\_a}^{2}+\textit {\_a} -1}d \textit {\_a} +\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.136 (sec). Leaf size: 91

ode=(x^2+2 x y[x]-y[x]^2)D[y[x],x]+x^2-2 x y[x]+y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\&,\frac {\text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-2 \text {$\#$1} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2-6 \text {$\#$1}+1}\&\right ]=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 - 2*x*y(x) + (x**2 + 2*x*y(x) - y(x)**2)*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out