3.209   ODE No. 209

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

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

Mathematica: cpu = 0.021003 (sec), leaf count = 84 \[ \left \{\left \{y(x)\to -\frac {\sqrt {2 a^2 c_1 x+a^2 c_1^2+a^2 x^2-b}}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt {2 a^2 c_1 x+a^2 c_1^2+a^2 x^2-b}}{\sqrt {a}}\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 21 \[ \left \{ x-{\frac {1}{a}\sqrt {a \left ( y \left ( x \right ) \right ) ^{ 2}+b}}+{\it \_C1}=0 \right \} \]