3.386   ODE No. 386

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

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

Mathematica: cpu = 0.204526 (sec), leaf count = 56 \[ \left \{\left \{y(x)\to 2 a e^{2 c_1} \left (4 e^{2 c_1}+x^2\right )\right \},\left \{y(x)\to \frac {e^{2 c_1} \left (e^{2 c_1}-2 a x^2\right )}{8 a}\right \}\right \} \]

Maple: cpu = 0.655 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{4}}{8}},y \left ( x \right ) ={x}^{2}{\it \_C1}+2\,{\frac {{{\it \_C1}}^{2}}{a}} \right \} \]