2.310   ODE No. 310

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

\[ x^3+\left (5 x^2 y(x)+2 y(x)^3\right ) y'(x)+5 x y(x)^2=0 \] Mathematica : cpu = 0.191035 (sec), leaf count = 159

\[\left \{\left \{y(x)\to -\frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \}\right \}\] Maple : cpu = 0.151 (sec), leaf count = 125

\[\left \{y \left (x \right ) = -\frac {\sqrt {-10 c_{1} x^{2}-2 \sqrt {23 x^{4} c_{1}^{2}+2}}}{2 \sqrt {c_{1}}}, y \left (x \right ) = \frac {\sqrt {-10 c_{1} x^{2}-2 \sqrt {23 x^{4} c_{1}^{2}+2}}}{2 \sqrt {c_{1}}}, y \left (x \right ) = -\frac {\sqrt {-10 c_{1} x^{2}+2 \sqrt {23 x^{4} c_{1}^{2}+2}}}{2 \sqrt {c_{1}}}, y \left (x \right ) = \frac {\sqrt {-10 c_{1} x^{2}+2 \sqrt {23 x^{4} c_{1}^{2}+2}}}{2 \sqrt {c_{1}}}\right \}\]