60.1.148 problem 151

Internal problem ID [10162]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 151
Date solved : Sunday, March 30, 2025 at 03:20:43 PM
CAS classification : [_rational, _Abel]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 65

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

\[ c_1 +\frac {x}{{\left (\frac {\left (x^{2}+1\right ) \left (y^{2}+1\right )}{\left (x y-1\right )^{2}}\right )}^{{1}/{4}}}+\frac {\left (x +y\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (x +y\right )^{2}}{\left (x y-1\right )^{2}}\right )}{2 x y-2} = 0 \]

✓ Mathematica. Time used: 0.427 (sec). Leaf size: 203

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

\[ \text {Solve}\left [c_1=\frac {\frac {1}{2} \left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right ) \sqrt [4]{1-\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2} \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {5}{4},\frac {3}{2},\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2}},y(x)\right ] \]

✗ Sympy

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

Timed Out