2.543   ODE No. 543

$x \left (x^2+1\right ) y'(x)-x^2 y(x)+y(x)^3 \left (-y'(x)^2\right )+x y(x)^2 y'(x)^3=0$ Mathematica : cpu = 0.0239505 (sec), leaf count = 55

$\left \{\left \{y(x)\to -\sqrt {c_1 x^2+\frac {c_1}{c_1{}^2+1}}\right \},\left \{y(x)\to \sqrt {c_1 x^2+\frac {c_1}{c_1{}^2+1}}\right \}\right \}$ Maple : cpu = 1.089 (sec), leaf count = 277

$\left \{ y \left ( x \right ) =-{\frac {i}{2}}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2-2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}},y \left ( x \right ) =-{\frac {i}{2}}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2+2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}},y \left ( x \right ) ={\frac {i}{2}}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2-2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}},y \left ( x \right ) ={\frac {i}{2}}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2+2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2-2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}}},y \left ( x \right ) ={\frac {1}{2}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2-2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2+2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}}},y \left ( x \right ) ={\frac {1}{2}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2+2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}}} \right \}$