3.310   ODE No. 310

\[ \boxed { \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3}+5\,{x}^{2}y \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +5\,x \left ( y \left ( x \right ) \right ) ^{2}+{x}^{3}=0} \]

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

Mathematica: cpu = 0.044006 (sec), leaf count = 159 \[ \left \{\left \{y(x)\to -\frac {\sqrt {-\sqrt {2 e^{4 c_1}+23 x^4}-5 x^2}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-\sqrt {2 e^{4 c_1}+23 x^4}-5 x^2}}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {\sqrt {2 e^{4 c_1}+23 x^4}-5 x^2}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {\sqrt {2 e^{4 c_1}+23 x^4}-5 x^2}}{\sqrt {2}}\right \}\right \} \]

Maple: cpu = 0.109 (sec), leaf count = 125 \[ \left \{ y \left ( x \right ) =-{\frac {1}{2}\sqrt {-10\,{x}^{2}{\it \_C1}-2\,\sqrt {23\,{x}^{4}{{\it \_C1}}^{2}+2}}{\frac {1}{\sqrt {{\it \_C1}}}}},y \left ( x \right ) ={\frac {1}{2}\sqrt {-10\,{x}^{2}{\it \_C1}-2\,\sqrt {23\,{x}^{4}{{\it \_C1}}^{2}+2}}{\frac {1}{\sqrt {{\it \_C1}}}}},y \left ( x \right ) =-{\frac {1}{2}\sqrt {-10\,{x}^{2}{\it \_C1}+2\,\sqrt {23\,{x}^{4}{{\it \_C1}}^{2}+2}}{\frac {1}{\sqrt {{\it \_C1}}}}},y \left ( x \right ) ={\frac {1}{2}\sqrt {-10\,{x}^{2}{\it \_C1}+2\,\sqrt {23\,{x}^{4}{{\it \_C1}}^{2}+2}}{\frac {1}{\sqrt {{\it \_C1}}}}} \right \} \]