2.315   ODE No. 315

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

\[ \left (2 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3-\text {Global$\grave { }$x}^4\right ) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+2 \text {Global$\grave { }$x}^3 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})-\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^4=0 \] Mathematica : cpu = 0.108128 (sec), leaf count = 368

\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\sqrt [3]{\frac {2}{3}} e^{c_1} \text {Global$\grave { }$x}}{\sqrt [3]{\sqrt {3} \sqrt {27 \text {Global$\grave { }$x}^6-4 e^{3 c_1} \text {Global$\grave { }$x}^3}-9 \text {Global$\grave { }$x}^3}}+\frac {\sqrt [3]{\sqrt {3} \sqrt {27 \text {Global$\grave { }$x}^6-4 e^{3 c_1} \text {Global$\grave { }$x}^3}-9 \text {Global$\grave { }$x}^3}}{\sqrt [3]{2} 3^{2/3}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to -\frac {\left (1+i \sqrt {3}\right ) e^{c_1} \text {Global$\grave { }$x}}{2^{2/3} \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {27 \text {Global$\grave { }$x}^6-4 e^{3 c_1} \text {Global$\grave { }$x}^3}-9 \text {Global$\grave { }$x}^3}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {3} \sqrt {27 \text {Global$\grave { }$x}^6-4 e^{3 c_1} \text {Global$\grave { }$x}^3}-9 \text {Global$\grave { }$x}^3}}{2 \sqrt [3]{2} 3^{2/3}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to -\frac {\left (1-i \sqrt {3}\right ) e^{c_1} \text {Global$\grave { }$x}}{2^{2/3} \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {27 \text {Global$\grave { }$x}^6-4 e^{3 c_1} \text {Global$\grave { }$x}^3}-9 \text {Global$\grave { }$x}^3}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {3} \sqrt {27 \text {Global$\grave { }$x}^6-4 e^{3 c_1} \text {Global$\grave { }$x}^3}-9 \text {Global$\grave { }$x}^3}}{2 \sqrt [3]{2} 3^{2/3}}\right \}\right \}\]

Maple : cpu = 0.088 (sec), leaf count = 447

\[ \left \{ y \left ( x \right ) ={\frac {\sqrt [3]{12}}{6\,{\it \_C1}}\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}+{\frac {x{12}^{{\frac {2}{3}}}}{6}{\frac {1}{\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}},y \left ( x \right ) =-{\frac {\sqrt [3]{12}}{12\,{\it \_C1}}\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}-{\frac {x{12}^{{\frac {2}{3}}}}{12}{\frac {1}{\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {\sqrt [3]{12}}{6\,{\it \_C1}}\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}-{\frac {x{12}^{{\frac {2}{3}}}}{6}{\frac {1}{\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}} \right ) ,y \left ( x \right ) =-{\frac {\sqrt [3]{12}}{12\,{\it \_C1}}\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}-{\frac {x{12}^{{\frac {2}{3}}}}{12}{\frac {1}{\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {\sqrt [3]{12}}{6\,{\it \_C1}}\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}-{\frac {x{12}^{{\frac {2}{3}}}}{6}{\frac {1}{\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}} \right ) \right \} \]