2.300   ODE No. 300

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

\[ 6 x y(x)^2 y'(x)+2 y(x)^3+x=0 \] Mathematica : cpu = 0.100385 (sec), leaf count = 99

\[\left \{\left \{y(x)\to \frac {\sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}}\right \}\right \}\] Maple : cpu = 0.025 (sec), leaf count = 83

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