60.1.297 problem 303

Internal problem ID [10311]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 303
Date solved : Wednesday, March 05, 2025 at 10:10:52 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x y-1\right )^{2} x y^{\prime }+\left (x^{2} y^{2}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.168 (sec). Leaf size: 34

ode:=(x*y(x)-1)^2*x*diff(y(x),x)+(x^2*y(x)^2+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+2 c_{1} {\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x} \]

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 25

ode=(x*y[x]-1)^2*x*D[y[x],x]+(x^2*y[x]^2+1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x y(x)-\frac {1}{x y(x)}-2 \log (y(x))=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.234 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x*y(x) - 1)**2*Derivative(y(x), x) + (x**2*y(x)**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \frac {x y{\left (x \right )}}{2} - \log {\left (x \right )} + \log {\left (x y{\left (x \right )} \right )} + \frac {1}{2 x y{\left (x \right )}} = C_{1} \]