2.663   ODE No. 663

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

\[ y'(x)=\frac {x^2 \sqrt {4 a x-y(x)^2}+2 a}{y(x)} \] Mathematica : cpu = 1.52554 (sec), leaf count = 101

\[\left \{\left \{y(x)\to -\frac {\sqrt {-4096 a^6 x^6+128 a^3 e^{c_1} x^3+147456 a^7 x-e^{2 c_1}}}{192 a^3}\right \},\left \{y(x)\to \frac {\sqrt {-4096 a^6 x^6+128 a^3 e^{c_1} x^3+147456 a^7 x-e^{2 c_1}}}{192 a^3}\right \}\right \}\] Maple : cpu = 0.251 (sec), leaf count = 27

\[ \left \{ -\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}-{\frac {{x}^{3}}{3}}-{\it \_C1}=0 \right \} \]