2.306   ODE No. 306

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \left (y(x)^3-x^3\right ) y'(x)-x^2 y(x)=0 \] Mathematica : cpu = 0.135852 (sec), leaf count = 201

\[\left \{\left \{y(x)\to \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{x^3+\sqrt {x^6-e^{6 c_1}}}\right \}\right \}\] Maple : cpu = 0.27 (sec), leaf count = 231

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