2.306   ODE No. 306

$\left (y(x)^3-x^3\right ) y'(x)-x^2 y(x)=0$ Mathematica : cpu = 0.113539 (sec), leaf count = 201

$\left \{\left \{y(x)\to \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to \sqrt [3]{\sqrt {x^6-e^{6 c_1}}+x^3}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{\sqrt {x^6-e^{6 c_1}}+x^3}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{\sqrt {x^6-e^{6 c_1}}+x^3}\right \}\right \}$ Maple : cpu = 0.299 (sec), leaf count = 231

$\left \{ y \left ( x \right ) ={x{\frac {1}{\sqrt [3]{- \left ( {\it \_C1}\,{x}^{3}-\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) ={x{\frac {1}{\sqrt [3]{- \left ( {\it \_C1}\,{x}^{3}+\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) =4\,{\frac {x}{ \left ( 1+i\sqrt {3} \right ) ^{2}\sqrt [3]{- \left ( {\it \_C1}\,{x}^{3}-\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}},y \left ( x \right ) =4\,{\frac {x}{ \left ( 1+i\sqrt {3} \right ) ^{2}\sqrt [3]{- \left ( {\it \_C1}\,{x}^{3}+\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}},y \left ( x \right ) =4\,{\frac {x}{ \left ( i\sqrt {3}-1 \right ) ^{2}\sqrt [3]{- \left ( {\it \_C1}\,{x}^{3}-\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}},y \left ( x \right ) =4\,{\frac {x}{ \left ( i\sqrt {3}-1 \right ) ^{2}\sqrt [3]{- \left ( {\it \_C1}\,{x}^{3}+\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}} \right \}$