2.436   ODE No. 436

\[ -x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0 \]

✓ Mathematica : cpu = 0.0876419 (sec), leaf count = 115

DSolve[-x^4 + (1 - x^2)*y[x]^2 - 2*x*y[x]*Derivative[1][y][x] + x^2*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {x \tanh (x-c_1)}{\sqrt {1-\tanh ^2(x-c_1)}}\right \},\left \{y(x)\to \frac {x \tanh (x-c_1)}{\sqrt {1-\tanh ^2(x-c_1)}}\right \},\left \{y(x)\to -\frac {x \tanh (x+c_1)}{\sqrt {1-\tanh ^2(x+c_1)}}\right \},\left \{y(x)\to \frac {x \tanh (x+c_1)}{\sqrt {1-\tanh ^2(x+c_1)}}\right \}\right \}\]

✓ Maple : cpu = 1.1 (sec), leaf count = 61

dsolve(x^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+y(x)^2*(-x^2+1)-x^4 = 0,y(x))
 

\[y \left (x \right ) = -i x\]